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Volumn 11, Issue 1, 2010, Pages 79-87

Global H1 solvability of the 3D logarithmic Schrödinger equation

Author keywords

Global solvability; Logarithmic nonlinearities; Nonlinear Schr dinger equation; Quantum mechanics

Indexed keywords

DINGER EQUATION; GLOBAL SOLVABILITY; INITIAL-BOUNDARY VALUE PROBLEMS; LOGARITHMIC NONLINEARITIES; MILD SOLUTION; QUANTUM MECHANICS;

EID: 70350716926     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.10.017     Document Type: Article
Times cited : (73)

References (27)
  • 1
    • 0001323666 scopus 로고
    • Un théorème de compacité
    • Aubin J.P. Un théorème de compacité. C. R. Acad. Sci., Sér. I 256 (1963) 5042-5044
    • (1963) C. R. Acad. Sci., Sér. , vol.I 256 , pp. 5042-5044
    • Aubin, J.P.1
  • 2
    • 7544228429 scopus 로고    scopus 로고
    • An analysis of quantum Fokker-Planck models: A Wigner function approach
    • Arnold A., López J.L., Markowich P.A., and Soler J. An analysis of quantum Fokker-Planck models: A Wigner function approach. Rev. Mat. Iberoamericana 20 (2004) 771-814
    • (2004) Rev. Mat. Iberoamericana , vol.20 , pp. 771-814
    • Arnold, A.1    López, J.L.2    Markowich, P.A.3    Soler, J.4
  • 4
    • 0040522777 scopus 로고    scopus 로고
    • 2 Solutions to the Schrödinger-Poisson System: Existence, uniqueness, time behaviour, and smoothing effects
    • 2 Solutions to the Schrödinger-Poisson System: Existence, uniqueness, time behaviour, and smoothing effects. Math. Models Methods Appl. Sci. 8 (1997) 1051-1083
    • (1997) Math. Models Methods Appl. Sci. , vol.8 , pp. 1051-1083
    • Castella, F.1
  • 5
    • 0003197180 scopus 로고
    • An introduction to nonlinear Schrödinger equations
    • Río de Janeiro
    • Cazenave T. An introduction to nonlinear Schrödinger equations. Textos de Métodos Matemáticos vol. 22 (1989), Río de Janeiro
    • (1989) Textos de Métodos Matemáticos , vol.22
    • Cazenave, T.1
  • 6
    • 0039683992 scopus 로고
    • Stable solutions of the logarithmic Schrödinger equation
    • Cazenave T. Stable solutions of the logarithmic Schrödinger equation. Nonlinear Anal. 7 (1983) 1127-1140
    • (1983) Nonlinear Anal. , vol.7 , pp. 1127-1140
    • Cazenave, T.1
  • 7
    • 0002528717 scopus 로고
    • Equations d'évolution avec non linéarité logarithmique
    • Cazenave T., and Haraux A. Equations d'évolution avec non linéarité logarithmique. Ann. Fac. Sci. Univ. Toulouse 2 (1980) 21-55
    • (1980) Ann. Fac. Sci. Univ. Toulouse , vol.2 , pp. 21-55
    • Cazenave, T.1    Haraux, A.2
  • 9
    • 0035738259 scopus 로고    scopus 로고
    • Comments on the nonlinear Schrödinger equation
    • Davidson M.P. Comments on the nonlinear Schrödinger equation. Il Nuovo Cimento B V116B (2001) 1291-1296
    • (2001) Il Nuovo Cimento B , vol.V116B , pp. 1291-1296
    • Davidson, M.P.1
  • 10
    • 0000103833 scopus 로고
    • On a general nonlinear Schrödinger equation admitting diffusion currents
    • Doebner H.D., and Goldin G.A. On a general nonlinear Schrödinger equation admitting diffusion currents. Phys. Lett. A 162 (1992) 397-401
    • (1992) Phys. Lett. A , vol.162 , pp. 397-401
    • Doebner, H.D.1    Goldin, G.A.2
  • 11
    • 60949097144 scopus 로고    scopus 로고
    • Soliton-like solutions for a capillary fluid, Waves and Stability in Continuous Media
    • S. De Martino, G. Lauro, Soliton-like solutions for a capillary fluid, Waves and Stability in Continuous Media, in: Proceedings of the 12th Conference on WASCOM, 2003
    • (2003) Proceedings of the 12th Conference on WASCOM
    • De Martino, S.1    Lauro, G.2
  • 12
    • 0042864664 scopus 로고    scopus 로고
    • Logarithmic Schrödinger-like equation as a model for magma transport
    • De Martino S., Falanga M., Godano C., and Lauro G. Logarithmic Schrödinger-like equation as a model for magma transport. Europhys. Lett. 63 (2003) 472-475
    • (2003) Europhys. Lett. , vol.63 , pp. 472-475
    • De Martino, S.1    Falanga, M.2    Godano, C.3    Lauro, G.4
  • 13
    • 33644794189 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • Evans L.C. Partial Differential Equations. Graduate Studies in Mathematics vol. 19 (1998), American Mathematical Society, Providence, RI
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 14
    • 0028413338 scopus 로고
    • The quantum hydrodynamic model for semiconductor devices
    • Gardner C. The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math. 54 (1994) 409-427
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 409-427
    • Gardner, C.1
  • 15
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger Equations. I and II
    • 1-32, 33-71
    • Ginibre J., and Velo G. On a class of nonlinear Schrödinger Equations. I and II. J. Funct. Anal. 32 1 (1979) 1-32, 33-71
    • (1979) J. Funct. Anal. , vol.32 , Issue.1
    • Ginibre, J.1    Velo, G.2
  • 16
    • 0041675189 scopus 로고
    • Application of the nonlinear Schrödinger equation with a logarithmic inhomogeneous term to nuclear physics
    • Hefter E.F. Application of the nonlinear Schrödinger equation with a logarithmic inhomogeneous term to nuclear physics. Phys. Rev. A 32 (1985) 1201-1204
    • (1985) Phys. Rev. A , vol.32 , pp. 1201-1204
    • Hefter, E.F.1
  • 17
    • 0036000665 scopus 로고    scopus 로고
    • Local existence of solutions to the transient quantum hydrodynamic equations
    • Jüngel A., Mariani M.C., and Rial D. Local existence of solutions to the transient quantum hydrodynamic equations. Math. Models Methods Appl. Sci. 12 (2002) 485-495
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , pp. 485-495
    • Jüngel, A.1    Mariani, M.C.2    Rial, D.3
  • 18
    • 36849110255 scopus 로고
    • On the Schrödinger-Langevin equation
    • Kostin M.D. On the Schrödinger-Langevin equation. J. Chem. Phys. 57 (1972) 3589-3591
    • (1972) J. Chem. Phys. , vol.57 , pp. 3589-3591
    • Kostin, M.D.1
  • 19
    • 70350744399 scopus 로고
    • Dissipative forces and the algebra of operators in stochastic quantum mechanics
    • Lemos N.A. Dissipative forces and the algebra of operators in stochastic quantum mechanics. Phys. Lett. A 78 (1980) 239-241
    • (1980) Phys. Lett. A , vol.78 , pp. 239-241
    • Lemos, N.A.1
  • 20
    • 37649027518 scopus 로고    scopus 로고
    • Nonlinear Ginzburg-Landau-type approach to quantum dissipation
    • López J.L. Nonlinear Ginzburg-Landau-type approach to quantum dissipation. Phys. Rev. E. 69 (2004) 026110
    • (2004) Phys. Rev. E. , vol.69 , pp. 026110
    • López, J.L.1
  • 21
    • 70350720652 scopus 로고    scopus 로고
    • A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics
    • in press
    • J.L. López, J. Montejo-Gámez, A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics, Physica D (in press)
    • Physica D
    • López, J.L.1    Montejo-Gámez, J.2
  • 22
    • 0034392770 scopus 로고    scopus 로고
    • Asymptotic behaviour to the 3-D Schrödinger/Hartree-Poisson and Wigner-Poisson systems
    • López J.L., and Soler J. Asymptotic behaviour to the 3-D Schrödinger/Hartree-Poisson and Wigner-Poisson systems. Math. Models Methods Appl. Sci. 10 6 (2000) 923-943
    • (2000) Math. Models Methods Appl. Sci. , vol.10 , Issue.6 , pp. 923-943
    • López, J.L.1    Soler, J.2
  • 23
    • 4243766905 scopus 로고
    • New method for the solution of the logarithmic nonlinear Schrödinger equation via stochastic mechanics
    • Nassar A.B. New method for the solution of the logarithmic nonlinear Schrödinger equation via stochastic mechanics. Phys. Rev. A 33 (1985) 3502-3505
    • (1985) Phys. Rev. A , vol.33 , pp. 3502-3505
    • Nassar, A.B.1
  • 24
    • 36049058883 scopus 로고
    • Derivation of the Schrödinger equation from Newtonian Mechanics
    • Nelson E. Derivation of the Schrödinger equation from Newtonian Mechanics. Phys. Rev 150 (1966) 1079-1085
    • (1966) Phys. Rev , vol.150 , pp. 1079-1085
    • Nelson, E.1
  • 25
    • 0039895644 scopus 로고    scopus 로고
    • High-field limit for the Vlasov-Poisson-Fokker-Planck system
    • Nieto J., Poupaud F., and Soler J. High-field limit for the Vlasov-Poisson-Fokker-Planck system. Arch. Ration. Mech. Anal. 158 (2001) 29-59
    • (2001) Arch. Ration. Mech. Anal. , vol.158 , pp. 29-59
    • Nieto, J.1    Poupaud, F.2    Soler, J.3
  • 26
    • 29344431971 scopus 로고
    • Springer-Verlag
    • Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences vol. 44 (1983), Springer-Verlag
    • (1983) Applied Mathematical Sciences , vol.44
    • Pazy, A.1
  • 27
    • 0001974832 scopus 로고
    • Multidimensional nonlinear Schrödinger equations with exponentially confined solutions
    • Sabatier P.C. Multidimensional nonlinear Schrödinger equations with exponentially confined solutions. Inverse Problems 6 (1990) L47-L53
    • (1990) Inverse Problems , vol.6
    • Sabatier, P.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.