메뉴 건너뛰기




Volumn , Issue , 2004, Pages

Highly oscillatory partial differential equations

Author keywords

[No Author keywords available]

Indexed keywords

LOW-TEMPERATURE PHYSICS; PARTIAL DIFFERENTIAL EQUATIONS (PDE); SEMI-CLASSICAL ASYMPTOTICS; WIGNER TRANSFORMS;

EID: 3042710051     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (1)

References (99)
  • 1
    • 0000950371 scopus 로고
    • On the intensity of light in a neighborhood of a caustic
    • G. B. Airy; On the intensity of light in a neighborhood of a caustic, Trans. Cambr. Philos. Soc. 6 (1938), pp. 379-403.
    • (1938) Trans. Cambr. Philos. Soc. , vol.6 , pp. 379-403
    • Airy, G.B.1
  • 2
    • 0033074557 scopus 로고    scopus 로고
    • High frequency approximation of solutions to critical nonlinear wave eqautions
    • H. Bahouri, P. Gérard; High frequency approximation of solutions to critical nonlinear wave eqautions, Amer. J. Math. 121 (1999), no. 1, pp. 131-175.
    • (1999) Amer. J. Math. , vol.121 , Issue.1 , pp. 131-175
    • Bahouri, H.1    Gérard, P.2
  • 4
    • 0037408314 scopus 로고    scopus 로고
    • Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation
    • to appear in
    • W. Bao, D. Jaksch, P. A. Markowich; Numerical solution of the Gross-Pitaevskii Equation for Bose-Einstein condensation, to appear in J. Comput. Phys. (2003).
    • (2003) J. Comput. Phys.
    • Bao, W.1    Jaksch, D.2    Markowich, P.A.3
  • 5
    • 0037138007 scopus 로고    scopus 로고
    • On time-splitting spectral approximations for the Schrödinger equation in the semi-classical regime
    • W. Bao, S. Jin, P. A. Markowich; On time-splitting spectral approximations for the Schrödinger equation in the semi-classical regime, J. Comput. Phys. 175 (2002), no. 2, pp. 487-524.
    • (2002) J. Comput. Phys. , vol.175 , Issue.2 , pp. 487-524
    • Bao, W.1    Jin, S.2    Markowich, P.A.3
  • 6
    • 1842531889 scopus 로고    scopus 로고
    • Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semi-classical regimes
    • to appear in
    • W. Bao, S. Jin, P. A. Markowich; Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semi-classical regimes, to appear in SIAM J. of Comp. (2003).
    • (2003) SIAM J. of Comp.
    • Bao, W.1    Jin, S.2    Markowich, P.A.3
  • 7
    • 0033421722 scopus 로고    scopus 로고
    • Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations
    • J. D. Benamou; Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations, Comm. Pure Appl. Math. 52 (1999), pp. 1443-1475.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 1443-1475
    • Benamou, J.D.1
  • 10
    • 34250940025 scopus 로고
    • Über die Quantenmechanik der Elektronen in Kristallgittern
    • F. Bloch; Über die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys. 52 (1928), pp. 555-600.
    • (1928) Z. Phys. , vol.52 , pp. 555-600
    • Bloch, F.1
  • 11
    • 0348098932 scopus 로고    scopus 로고
    • A semiclassical approach to the Dirac equation
    • J. Boite, S. Keppeler; A semiclassical approach to the Dirac equation, Ann. Phys. 274 (1999), pp. 125-162.
    • (1999) Ann. Phys. , vol.274 , pp. 125-162
    • Boite, J.1    Keppeler, S.2
  • 12
    • 0001183792 scopus 로고    scopus 로고
    • A kinetic formulation for multibranch entropy solutions of scalar conservation laws
    • Y. Brenier, L. Corrias; A kinetic formulation for multibranch entropy solutions of scalar conservation laws, Henri Poincaré, Analyse non linéare 15 (1998), pp. 169-190.
    • (1998) Henri Poincaré, Analyse Non Linéare , vol.15 , pp. 169-190
    • Brenier, Y.1    Corrias, L.2
  • 13
    • 0001385049 scopus 로고
    • Notes on undulatory mechanics
    • L. Brillouin; Notes on undulatory mechanics, J. Phys. 7 (1926), pp. 353-365.
    • (1926) J. Phys. , vol.7 , pp. 353-365
    • Brillouin, L.1
  • 14
    • 84862372662 scopus 로고    scopus 로고
    • Mesures Semi-classique et Mesures de Défaut
    • N. Burq; Mesures Semi-Classique et Mesures de Défaut, Séminaire Bourbaki no. 826 (1997).
    • (1997) Séminaire Bourbaki No. 826 , vol.826
    • Burq, N.1
  • 16
    • 0001605822 scopus 로고    scopus 로고
    • Geometric optics with caustic crossing for some nonlinear Schrödinger equations
    • R. Carles; Geometric optics with caustic crossing for some nonlinear Schrödinger equations, Indiana Univ. Math. J. 49, (2000), no. 2, pp. 475-551.
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.2 , pp. 475-551
    • Carles, R.1
  • 17
    • 0041738243 scopus 로고    scopus 로고
    • Remarques sur les mesures de Wigner
    • R. Carles; Remarques sur les mesures de Wigner, C. R. Acad. Sci. Paris 332 (2001), pp. 981-984.
    • (2001) C. R. Acad. Sci. Paris , vol.332 , pp. 981-984
    • Carles, R.1
  • 18
    • 0141814240 scopus 로고    scopus 로고
    • Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
    • R. Carles; Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation, Ann. Henri Poincaré, Analyse non linéare 20 (2003), no. 3, pp. 501-542.
    • (2003) Ann. Henri Poincaré, Analyse Non Linéare , vol.20 , Issue.3 , pp. 501-542
    • Carles, R.1
  • 19
    • 0141503425 scopus 로고    scopus 로고
    • On the role of quadratic oscillations in nonlinear Schrödinger equations
    • to appear in
    • R. Carles, C. Fermanian-Kammerer, I. Gallagher; On the role of quadratic oscillations in nonlinear Schrödinger equations, to appear in J. Funct. Anal (2003).
    • (2003) J. Funct. Anal
    • Carles, R.1    Fermanian-Kammerer, C.2    Gallagher, I.3
  • 20
    • 0036660544 scopus 로고    scopus 로고
    • Rigorous derivation of the nonlinear Schrödinger equation and Davey-Stewartson systems from quadratic hyperbolic systems
    • T. Colin; Rigorous derivation of the nonlinear Schrödinger equation and Davey-Stewartson systems from quadratic hyperbolic systems, Asympt. Anal. 31 (2002), pp. 69-91.
    • (2002) Asympt. Anal. , vol.31 , pp. 69-91
    • Colin, T.1
  • 21
    • 0031352502 scopus 로고    scopus 로고
    • Homogenization of periodic structures via Bloch decomposition
    • C. Conca, M. Vanninathan; Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math. 57 (1997), no. 6, pp. 1639-1659.
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.6 , pp. 1639-1659
    • Conca, C.1    Vanninathan, M.2
  • 22
    • 0000466871 scopus 로고    scopus 로고
    • Periodic homogenization of Hamilton-Jacobi equations I: Additive eigenvalues and variational formula
    • M. Concordel; Periodic homogenization of Hamilton-Jacobi equations I: additive eigenvalues and variational formula, Indiana Univ. Math. J. 45 (1996), pp. 1095-1117.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 1095-1117
    • Concordel, M.1
  • 23
    • 21744440870 scopus 로고    scopus 로고
    • Periodic homogenization of Hamilton-Jacobi equations II: Eikonal equations
    • M. Concordel; Periodic homogenization of Hamilton-Jacobi equations II: eikonal equations, Proc. Roy. Soc. Edinburgh 127 (1997), pp. 665-689.
    • (1997) Proc. Roy. Soc. Edinburgh , vol.127 , pp. 665-689
    • Concordel, M.1
  • 24
    • 0001670086 scopus 로고
    • Wave packets and Fourier integral operators
    • A. Cordoba, C. Fefferman; Wave packets and Fourier integral operators, Comm. Part. Diff. Equ. 3 (1978), pp. 979-1005.
    • (1978) Comm. Part. Diff. Equ. , vol.3 , pp. 979-1005
    • Cordoba, A.1    Fefferman, C.2
  • 25
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. Crandall, P. L. Lions; Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. Math. Soc. 277 (1983), no. 1, pp. 1-42.
    • (1983) Trans. Am. Math. Soc. , vol.277 , Issue.1 , pp. 1-42
    • Crandall, M.1    Lions, P.L.2
  • 26
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. Crandall, H. Ishii, P. L. Lions; User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc. 27 (1992), no.1, pp. 1-61.
    • (1992) Bull. Am. Math. Soc. , vol.27 , Issue.1 , pp. 1-61
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 27
    • 0000320652 scopus 로고
    • Compensated compactness and general systems of conservations laws
    • R. Di Perna; Compensated compactness and general systems of conservations laws, Trans. Amer. Math. Soc. 292 (1985), pp. 383-420.
    • (1985) Trans. Amer. Math. Soc. , vol.292 , pp. 383-420
    • Di Perna, R.1
  • 28
    • 34250110146 scopus 로고
    • The validity of nonlinear geometrical opitcs for weak solutions of conservations laws
    • R. Di Perna, A. Majda; The validity of nonlinear geometrical opitcs for weak solutions of conservations laws, Comm. Math. Phys. 98 (1985), pp. 313-347.
    • (1985) Comm. Math. Phys. , vol.98 , pp. 313-347
    • Di Perna, R.1    Majda, A.2
  • 29
    • 0031488769 scopus 로고    scopus 로고
    • Dispersive nonlinear geometrical optics
    • P. Donat, J. Rauch Dispersive nonlinear geometrical optics, J. Math. Phys. 38 (1997), pp. 1484-1523.
    • (1997) J. Math. Phys. , vol.38 , pp. 1484-1523
    • Donat, P.1    Rauch, J.2
  • 30
    • 84980174402 scopus 로고
    • Oscillatory integrals, lagrangian immersions and unfoldings of singularities
    • J. J. Duistermaat; Oscillatory integrals, Lagrangian immersions and unfoldings of singularities, Comm. Pure Appl. Math. XXVII (1974), pp. 207-281.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 207-281
    • Duistermaat, J.J.1
  • 31
    • 0001359817 scopus 로고
    • Fourier integral operators II
    • J. J. Duistermaat, L. Hörmander; Fourier integral operators II, Acta Math. 128 (1972), pp. 183-269.
    • (1972) Acta Math. , vol.128 , pp. 183-269
    • Duistermaat, J.J.1    Hörmander, L.2
  • 32
    • 0030551797 scopus 로고    scopus 로고
    • Geometry of the transport equation in multicomponent WKB approximations
    • C. Emmerich, A. Weinstein; Geometry of the transport equation in multicomponent WKB approximations, Comm. Math. Phys. 176 (1996), pp. 701-711.
    • (1996) Comm. Math. Phys. , vol.176 , pp. 701-711
    • Emmerich, C.1    Weinstein, A.2
  • 33
    • 84974059058 scopus 로고
    • Periodic homogenisation of certain fully nonlinear partial differential equations
    • L. C. Evans; Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 3-4, pp. 245-265.
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.120 , Issue.3-4 , pp. 245-265
    • Evans, L.C.1
  • 35
    • 6044253546 scopus 로고    scopus 로고
    • Partial differential equations V
    • Springer Verlag
    • V. M. Fedoryuk; Partial Differential Equations V, Encyclopidia of Math. Sci. 34, Springer Verlag (1999).
    • (1999) Encyclopidia of Math. Sci. , vol.34
    • Fedoryuk, V.M.1
  • 36
    • 0142021597 scopus 로고    scopus 로고
    • Semi-classical analysis of a Dirac equation without adiabatic decoupling
    • to appear in
    • C. Fermanian-Kammerer; Semi-classical analysis of a Dirac equation without adiabatic decoupling, to appear in Monatsh. f. Math. (2003).
    • (2003) Monatsh. F. Math.
    • Fermanian-Kammerer, C.1
  • 37
    • 0013386103 scopus 로고    scopus 로고
    • Mesures semi-classiques et croisement de modes
    • C. Fermanian-Kammerer, P. Gérard; Mesures semi-classiques et croisement de modes, Bull. Soc. Math. France, 130 (2002), no. 1, pp. 123-168.
    • (2002) Bull. Soc. Math. France , vol.130 , Issue.1 , pp. 123-168
    • Fermanian-Kammerer, C.1    Gérard, P.2
  • 38
    • 0141680711 scopus 로고    scopus 로고
    • A Landau-Zener formula for non-degenerated involutive codimension 3 crossings
    • to appear in
    • C. Fermanian-Kammerer, P. Gérard; A Landau-Zener formula for non-degenerated involutive codimension 3 crossings, to appear in Ann. Inst. Henri Poincaré (2003).
    • (2003) Ann. Inst. Henri Poincaré
    • Fermanian-Kammerer, C.1    Gérard, P.2
  • 39
    • 0003332429 scopus 로고
    • Harmonic analysis in phase space
    • Princeton Univ. Press
    • G. Fblland; Harmonic Analysis in Phase Space, Annals of Math. Studies 122, Princeton Univ. Press (1989).
    • (1989) Annals of Math. Studies , vol.122
    • Fblland, G.1
  • 40
    • 0000804295 scopus 로고
    • Oscillations and energy densities in the wave equation
    • G. A. Francfort, F. Murat; Oscillations and energy densities in the wave equation, Comm. Part. Diff. Equ. 17 (1992), no. 11-12, pp. 1785-1865.
    • (1992) Comm. Part. Diff. Equ. , vol.17 , Issue.11-12 , pp. 1785-1865
    • Francfort, G.A.1    Murat, F.2
  • 41
    • 0003002361 scopus 로고
    • On the homogenization of quasilinear divergence structure operators
    • N. Fusco, G. Moscariello; On the homogenization of quasilinear divergence structure operators, Annali Mat. Pura Appl. 146 (1987), pp. 1-13.
    • (1987) Annali Mat. Pura Appl. , vol.146 , pp. 1-13
    • Fusco, N.1    Moscariello, G.2
  • 42
    • 0002375163 scopus 로고    scopus 로고
    • Quantum hydrodynamics, wigner transform and the classical limit
    • I. Gasser, P. A. Markowich; Quantum Hydrodynamics, Wigner transform and the classical limit, Asympt. Anal. 14 (1997), pp. 97-116.
    • (1997) Asympt. Anal. , vol.14 , pp. 97-116
    • Gasser, I.1    Markowich, P.A.2
  • 43
    • 0000538578 scopus 로고    scopus 로고
    • A review of dispersive limits of (non)linear Schrödinger-type equations
    • I. Gasser, C. Lin, P.A. Markowich; A review of dispersive limits of (non)linear Schrödinger-type equations, Taiwanese J. Math. 4 (2000), no. 4, pp. 501-529.
    • (2000) Taiwanese J. Math. , vol.4 , Issue.4 , pp. 501-529
    • Gasser, I.1    Lin, C.2    Markowich, P.A.3
  • 44
    • 0001342333 scopus 로고
    • Microlocal defect measures
    • P. Gérard; Microlocal defect measures, Comm. Part. Diff. Equ. 16 (1991), pp. 1761-1794.
    • (1991) Comm. Part. Diff. Equ. , vol.16 , pp. 1761-1794
    • Gérard, P.1
  • 45
    • 84862379672 scopus 로고
    • Remarques sur l'analyse semi-classique de l'equation Schrödinger non linéaire
    • lecture no. XIII
    • P. Gérard; Remarques sur l'analyse semi-classique de l'equation Schrödinger non linéaire, Séminaire EDP de L'École Polytechnique (1992), lecture no. XIII.
    • (1992) Séminaire EDP de L'École Polytechnique
    • Gérard, P.1
  • 46
    • 0030579045 scopus 로고    scopus 로고
    • Oscillations and concentration effects in semilinear dispersive wave equations
    • P. Gérard; Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 141 (1996), no. 1, pp. 60-98.
    • (1996) J. Funct. Anal. , vol.141 , Issue.1 , pp. 60-98
    • Gérard, P.1
  • 48
    • 0037143007 scopus 로고    scopus 로고
    • Using K-branch entropy solutions for multivalued geometrical optics computations
    • L. Gosse; Using K-branch entropy solutions for multivalued geometrical optics computations, J. Comp. Physics 180 (2002), pp. 155-182.
    • (2002) J. Comp. Physics , vol.180 , pp. 155-182
    • Gosse, L.1
  • 51
    • 21944449213 scopus 로고    scopus 로고
    • Semi-classical limit of the nonlinear Schrödinger equation in small time
    • E. Grenier; Semi-classical limit of the nonlinear Schrödinger equation in small time, Proc. AMS 126 (1998), no. 2, pp. 523-530.
    • (1998) Proc. AMS , vol.126 , Issue.2 , pp. 523-530
    • Grenier, E.1
  • 52
    • 0001742215 scopus 로고
    • Semi-classical asymptotics in solid-state physics
    • J. C. Guillot, J. Ralston, E. Trubowitz; Semi-classical asymptotics in solid-state physics, Comm. Math. Phys. 116 (1988), pp.401-415.
    • (1988) Comm. Math. Phys. , vol.116 , pp. 401-415
    • Guillot, J.C.1    Ralston, J.2    Trubowitz, E.3
  • 55
    • 0035219337 scopus 로고    scopus 로고
    • Semi-classical limit for the Schrödinger equation with a short scale periodic potential
    • F. Hövermann, H. Spohn, S. Teufel; Semi-classical limit for the Schrödinger equation with a short scale periodic potential, Comm. Math. Phys. 215 (2001), pp. 609-629.
    • (2001) Comm. Math. Phys. , vol.215 , pp. 609-629
    • Hövermann, F.1    Spohn, H.2    Teufel, S.3
  • 56
    • 84990566608 scopus 로고
    • Weakly nonlinear high frequency waves
    • J. Hunter, J. Keller; Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), pp. 547-569.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 547-569
    • Hunter, J.1    Keller, J.2
  • 57
    • 0023422783 scopus 로고
    • Caustics of nonlinear waves
    • J. Hunter, J. Keller; Caustics of nonlinear waves, Wave motion 9 (1987), pp. 429-443.
    • (1987) Wave Motion , vol.9 , pp. 429-443
    • Hunter, J.1    Keller, J.2
  • 60
    • 0034259179 scopus 로고    scopus 로고
    • Transparent nonlinear geometric optics and the Maxwell-Block equations
    • J. L. Joly, G. Metivier, J. Rauch; Transparent nonlinear geometric optics and the Maxwell-Block equations, J. Diff. Equ. 166 (2000), pp. 175-250.
    • (2000) J. Diff. Equ. , vol.166 , pp. 175-250
    • Joly, J.L.1    Metivier, G.2    Rauch, J.3
  • 61
    • 0040933396 scopus 로고    scopus 로고
    • Nonlinear oscillations beyond caustics
    • J. L. Joly, G. Metivier, J. Rauch; Nonlinear oscillations beyond caustics, Comm. Pure Appl. Math. 49 (1996), no. 5, pp.443-527.
    • (1996) Comm. Pure Appl. Math. , vol.49 , Issue.5 , pp. 443-527
    • Joly, J.L.1    Metivier, G.2    Rauch, J.3
  • 62
    • 0036381905 scopus 로고    scopus 로고
    • Semi-classical limit of a class of Schrödinger equations with potential
    • S. Keraani; Semi-classical limit of a class of Schrödinger equations with potential, Comm. Partial Diff. Equ. 27 (2002), no. 3-4, pp. 693-704.
    • (2002) Comm. Partial Diff. Equ. , vol.27 , Issue.3-4 , pp. 693-704
    • Keraani, S.1
  • 63
    • 34250915737 scopus 로고
    • Wellenmechanik und Halbzahlige Quantisierung
    • H. Kramers; Wellenmechanik und Halbzahlige Quantisierung, Zeit. Phys 39 (1926), pp. 828-840.
    • (1926) Zeit. Phys , vol.39 , pp. 828-840
    • Kramers, H.1
  • 65
    • 84972538741 scopus 로고
    • Asymptotic solutions of oscillatory initial value problems
    • P. Lax; Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957), pp. 627-646.
    • (1957) Duke Math. J. , vol.24 , pp. 627-646
    • Lax, P.1
  • 66
    • 84990575581 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation I
    • P.D. Lax, C. Levermore; The small dispersion limit of the Korteweg-de Vries equation I, Comm. Pure Appl. Math. 36 (1983), no. 3, pp. 253-290.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.3 , pp. 253-290
    • Lax, P.D.1    Levermore, C.2
  • 67
    • 84990602637 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation II
    • P.D. Lax, C. Levermore; The small dispersion limit of the Korteweg-de Vries equation II, Comm. Pure Appl. Math. 36 (1983), no. 5, pp. 571-593.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.5 , pp. 571-593
    • Lax, P.D.1    Levermore, C.2
  • 68
    • 84990587869 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries equation III
    • P. D. Lax, C. Levermore; The small dispersion limit of the Korteweg-de Vries equation III, Comm. Pure Appl. Math. 36 (1983), no. 6, pp. 809-829.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.6 , pp. 809-829
    • Lax, P.D.1    Levermore, C.2
  • 69
    • 0033438093 scopus 로고    scopus 로고
    • The semi-classical limit of the defocusing NLS Hierarchy
    • P.D. Lax, C. Levermore; The semi-classical limit of the defocusing NLS Hierarchy, Comm. Pure Appl. Math. 52 (1999), pp. 613-654.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 613-654
    • Lax, P.D.1    Levermore, C.2
  • 71
    • 0041357028 scopus 로고    scopus 로고
    • Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting
    • to appear in
    • P. L. Lions, P. E. Souganidis; Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting, to appear in Comm. Pure Appl. Math. (2003).
    • (2003) Comm. Pure Appl. Math.
    • Lions, P.L.1    Souganidis, P.E.2
  • 72
    • 84981755544 scopus 로고
    • Uniform asymptotics near caustics
    • D. Ludwig; Uniform asymptotics near caustics, Comm. Pure Appl. Math. XIX (1966), pp. 215-250.
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 215-250
    • Ludwig, D.1
  • 73
    • 85129697344 scopus 로고    scopus 로고
    • The maxwell equations in a periodic medium: Homogenization of the energy density
    • P. A. Markowich, F. Poupaud; The Maxwell Equations in a Periodic Medium: Homogenization of the Energy Density, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), no. 2, pp. 301-324.
    • (1996) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.23 , Issue.2 , pp. 301-324
    • Markowich, P.A.1    Poupaud, F.2
  • 74
    • 0000269855 scopus 로고
    • The classical limit of a self-consistent quantum-vlasov equation in 3D
    • P. A. Markowich, N. Mauser; The classical limit of a self-consistent quantum-Vlasov equation in 3D, Math. Models Methods Appl. Sci. 3 (1993), no. 1, pp. 109-124.
    • (1993) Math. Models Methods Appl. Sci. , vol.3 , Issue.1 , pp. 109-124
    • Markowich, P.A.1    Mauser, N.2
  • 75
    • 36449006348 scopus 로고
    • A wigner-function approach to (semi) classical limits: Electrons in a periodic potential
    • P.A. Markowich, N. Mauser, F. Poupaud; A Wigner-function approach to (semi)classical limits: electrons in a periodic potential, J. Math. Phys. 35 (1994), no. 3, pp. 1066-1094.
    • (1994) J. Math. Phys. , vol.35 , Issue.3 , pp. 1066-1094
    • Markowich, P.A.1    Mauser, N.2    Poupaud, F.3
  • 76
    • 0033480955 scopus 로고    scopus 로고
    • Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
    • P. A. Markowich, P. Pietra, C. Pohl; Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit, Numer. Math. 81 (1999), no. 4, pp. 595-630.
    • (1999) Numer. Math. , vol.81 , Issue.4 , pp. 595-630
    • Markowich, P.A.1    Pietra, P.2    Pohl, C.3
  • 77
    • 0141645582 scopus 로고    scopus 로고
    • A wigner-measure analysis of the Dufort-Frankel scheme for the schrödinger equation
    • P. A. Markowich, P. Pietra, C. Pohl H.P. Summing; A Wigner-measure analysis of the Dufort-Frankel scheme for the Schrödinger equation, SIAM J. Numer. Anal. 40 (2002), no. 4, pp. 1281-1310.
    • (2002) SIAM J. Numer. Anal. , vol.40 , Issue.4 , pp. 1281-1310
    • Markowich, P.A.1    Pietra, P.2    Pohl, C.3    Summing, H.P.4
  • 79
    • 0034148496 scopus 로고    scopus 로고
    • Refraction of high-frequency waves density by sharp interfaces and semi-classical measures at the boundary
    • L. Miller; Refraction of high-frequency waves density by sharp interfaces and semi-classical measures at the boundary, J. Math Pures Appl (9) 79 (2000), no. 3, pp. 227-269.
    • (2000) J. Math Pures Appl (9) , vol.79 , Issue.3 , pp. 227-269
    • Miller, L.1
  • 80
    • 0003310103 scopus 로고    scopus 로고
    • Asymptotic solution of a Hamilton-Jacobi equation
    • G. Namah; Asymptotic solution of a Hamilton-Jacobi equation, Asympt. Anal. 12 (1996), no. 4, pp. 355-370.
    • (1996) Asympt. Anal. , vol.12 , Issue.4 , pp. 355-370
    • Namah, G.1
  • 82
    • 0040062089 scopus 로고    scopus 로고
    • Semi-classical limits in a crystal with external potentials and effective mass theorems
    • F. Poupaud, C. Ringhofer; Semi-classical limits in a crystal with external potentials and effective mass theorems, Comm. Part. Diff. Equ. 21 (1996), pp. 1897-1918.
    • (1996) Comm. Part. Diff. Equ. , vol.21 , pp. 1897-1918
    • Poupaud, F.1    Ringhofer, C.2
  • 83
    • 0142085383 scopus 로고    scopus 로고
    • Lectures on nonlinear geometrical optics
    • AMS
    • J. Rauch; Lectures on Nonlinear Geometrical Optics, IAS/Park City Math. Series 5, AMS (1999).
    • (1999) IAS/Park City Math. Series , vol.5
    • Rauch, J.1
  • 85
    • 35348855615 scopus 로고    scopus 로고
    • Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results
    • D. Robert; Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results, Helv. Phys. Acta 71 (1998), pp.44-116.
    • (1998) Helv. Phys. Acta , vol.71 , pp. 44-116
    • Robert, D.1
  • 86
    • 0034551460 scopus 로고    scopus 로고
    • Some new results in multiphase geometrical optics
    • O. Runborg; Some new results in multiphase geometrical optics, Math. Modeling and Num. Analysis 34 (2000), pp. 1203-1231.
    • (2000) Math. Modeling and Num. Analysis , vol.34 , pp. 1203-1231
    • Runborg, O.1
  • 87
    • 0009937623 scopus 로고    scopus 로고
    • Stochastic homogenization of Hamilton-Jacobi equations and some applications
    • P.E. Souganidis; Stochastic homogenization of Hamilton-Jacobi equations and some applications, Asympt. Anal. 20 (1999), pp. 1-11.
    • (1999) Asympt. Anal. , vol.20 , pp. 1-11
    • Souganidis, P.E.1
  • 88
    • 84887251437 scopus 로고    scopus 로고
    • Wigner functions vs WKB-methods in multivalued geometrical optics
    • C. Sparber, P. A. Markowich, N. Mauser; Wigner functions vs WKB-methods in multivalued geometrical optics, Asympt. Anal. 33 (2003), no. 2, pp. 153-187.
    • (2003) Asympt. Anal. , vol.33 , Issue.2 , pp. 153-187
    • Sparber, C.1    Markowich, P.A.2    Mauser, N.3
  • 89
    • 0142136718 scopus 로고    scopus 로고
    • Semi-classical asymptotics for the Dirac-Maxwell system
    • to appear in
    • C. Sparber, P.A. Markowich; Semi-classical Asymptotics for the Dirac-Maxwell system, to appear in J. Math. Phys. (2003).
    • (2003) J. Math. Phys.
    • Sparber, C.1    Markowich, P.A.2
  • 90
    • 0347112450 scopus 로고    scopus 로고
    • Semi-classical limit of the Dirac equation and spin precession
    • H. Spohn; Semi-classical limit of the Dirac equation and spin precession, Ann. Physics 282 (2000), no. 2, pp.420-431.
    • (2000) Ann. Physics , vol.282 , Issue.2 , pp. 420-431
    • Spohn, H.1
  • 91
    • 3042753273 scopus 로고
    • Oscillations in nonlinear partial differential equations: Compensated compactness and homogenization
    • AMS
    • L. Tartar; Oscillations in nonlinear partial differential equations: compensated compactness and homogenization, Lectures in Appl. Math. 23, AMS (1986).
    • (1986) Lectures in Appl. Math. , vol.23
    • Tartar, L.1
  • 92
    • 84974050752 scopus 로고
    • H-measures: A new approach for studying homogenization, oscillations and concentration effects in partial differential equations
    • L. Tartar; H-measures: a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), pp. 193-230.
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 193-230
    • Tartar, L.1
  • 93
    • 4344669019 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation
    • Springer
    • C. Sulem, P. L. Sulem; The nonlinear Schrödinger equation, Applied Math. Sciences 139, Springer (1999).
    • (1999) Applied Math. Sciences , vol.139
    • Sulem, C.1    Sulem, P.L.2
  • 94
    • 0347879158 scopus 로고    scopus 로고
    • Some homogenization and corrector results for nonlinear monotone operators
    • P. Wall; Some homogenization and corrector results for nonlinear monotone operators, J. Nonl. Math. Phys. 5 (1998), no. 3, pp. 331-348.
    • (1998) J. Nonl. Math. Phys. , vol.5 , Issue.3 , pp. 331-348
    • Wall, P.1
  • 95
    • 34250917346 scopus 로고
    • Eine Verallgemeinerung der Quantenbedingung für die Zwecke der Wellenmechanik
    • G. Wentzel; Eine Verallgemeinerung der Quantenbedingung für die Zwecke der Wellenmechanik, Zeit. Phys. 38 (1926), pp. 38-45.
    • (1926) Zeit. Phys. , vol.38 , pp. 38-45
    • Wentzel, G.1
  • 97
    • 33745014742 scopus 로고
    • On the quantum correction for the thermodynamical equilibrium
    • E. Wigner; On the quantum correction for the thermodynamical equilibrium, Phys. Rev. 40 (1932), pp. 742-759.
    • (1932) Phys. Rev. , vol.40 , pp. 742-759
    • Wigner, E.1
  • 98
    • 0001332554 scopus 로고
    • Non-adiabatic crossing of energy-levels
    • C. Zener; Non-adiabatic crossing of energy-levels, Proc. Roy. Soc. Lond. 137 (1932), pp. 696-702.
    • (1932) Proc. Roy. Soc. Lond. , vol.137 , pp. 696-702
    • Zener, C.1
  • 99
    • 0036100942 scopus 로고    scopus 로고
    • The limit from the Schrödinger-Poisson equation to the Vlasov-Poisson equation with general data in one dimension
    • P. Zhang, Y. Zheng, N. Mauser; The limit from the Schrödinger- Poisson equation to the Vlasov-Poisson equation with general data in one dimension, Comm. Pure Appl. Math. 55 (2002), no. 5, pp. 582-632.
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.5 , pp. 582-632
    • Zhang, P.1    Zheng, Y.2    Mauser, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.