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Volumn 37, Issue 1, 2005, Pages 103-126

Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms

Author keywords

Diffusion dispersion; Nonlocal free energy; Sharp interface limit; Undercompressive shock waves

Indexed keywords

DIFFUSION-DISPERSION; NONLOCAL FREE ENERGY; SHARP-INTERFACE LIMIT;

EID: 33144489184     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141004443300     Document Type: Article
Times cited : (17)

References (36)
  • 3
    • 0031282920 scopus 로고    scopus 로고
    • Traveling waves in a convolution model for phase transitions
    • P. BATES, P. FIFE, X. REN, AND X. WANG, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal., 138 (1997), pp. 105-136.
    • (1997) Arch. Rational Mech. Anal. , vol.138 , pp. 105-136
    • Bates, P.1    Fife, P.2    Ren, X.3    Wang, X.4
  • 4
    • 0037138002 scopus 로고    scopus 로고
    • Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws
    • N. BEDJAOUI AND P. LEFLOCH, Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws, J. Differential Equations, 178 (2002), pp. 574-607.
    • (2002) J. Differential Equations , vol.178 , pp. 574-607
    • Bedjaoui, N.1    Lefloch, P.2
  • 5
    • 0033265466 scopus 로고    scopus 로고
    • Stability of subsonic planar phase boundaries in a van der Waals fluid
    • S. BENZONI-GAVAGE, Stability of subsonic planar phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 150 (1999), pp. 23-55.
    • (1999) Arch. Rational Mech. Anal. , vol.150 , pp. 23-55
    • Benzoni-Gavage, S.1
  • 7
    • 0034353687 scopus 로고    scopus 로고
    • Existence of undercompressive traveling waves in thin film equations
    • A. BERTOZZI AND M. SHEARER, Existence of undercompressive traveling waves in thin film equations, SIAM J. Math. Anal., 32 (2000), pp. 194-213.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 194-213
    • Bertozzi, A.1    Shearer, M.2
  • 9
    • 21844481773 scopus 로고
    • Travelling fronts in non-local evolution equations
    • A. DE MASI, T. GOBRON, AND E. PRESUTTI, Travelling fronts in non-local evolution equations, Arch. Rational Mech. Anal., 132 (1995), pp. 143-205.
    • (1995) Arch. Rational Mech. Anal. , vol.132 , pp. 143-205
    • De Masi, A.1    Gobron, T.2    Presutti, E.3
  • 10
    • 0021835204 scopus 로고
    • Measure-valued solutions to conservation laws
    • R. DIPERNA, Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal., 88 (1985), pp. 223-270.
    • (1985) Arch. Rational Mech. Anal. , vol.88 , pp. 223-270
    • DiPerna, R.1
  • 11
    • 0021788792 scopus 로고
    • On the thermomechanics of interstitial working
    • J. DUNN AND J. SERRIN, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal., 88 (1985), pp. 95-133.
    • (1985) Arch. Rational Mech. Anal. , vol.88 , pp. 95-133
    • Dunn, J.1    Serrin, J.2
  • 12
    • 84971116294 scopus 로고
    • Existence and uniqueness of traveling waves for a neural network
    • Sect A
    • G. ERMENTROUT AND J. MCLEOD, Existence and uniqueness of traveling waves for a neural network, Proc. Roy. Soc. Edinburgh, 123 Sect A (1993), pp. 461-478.
    • (1993) Proc. Roy. Soc. Edinburgh , vol.123 , pp. 461-478
    • Ermentrout, G.1    Mcleod, J.2
  • 14
    • 15544370306 scopus 로고    scopus 로고
    • Dynamic flows with liquid/vapor phase transitions
    • S. Friedlander and D. Serre, eds., North-Holland, Amsterdam
    • H. FAN AND M. SLEMROD, Dynamic flows with liquid/vapor phase transitions, in Handbook of Mathematical Fluid Dynamics, S. Friedlander and D. Serre, eds., North-Holland, Amsterdam, 2002, pp. 373-420.
    • (2002) Handbook of Mathematical Fluid Dynamics , pp. 373-420
    • Fan, H.1    Slemrod, M.2
  • 15
    • 0032141408 scopus 로고    scopus 로고
    • On a model of nonlocal continuum mechanics Part I: Existence and regularity
    • R. FOSDICK AND D. MASON, On a model of nonlocal continuum mechanics Part I: Existence and regularity, SIAM J. Appl. Math., 58 (1998), pp. 1278-1306.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1278-1306
    • Fosdick, R.1    Mason, D.2
  • 17
    • 0020913387 scopus 로고
    • The viscosity-capillarity criterion for shocks and phase transitions
    • R. HAGAN AND M. SLEMROD, The viscosity-capillarity criterion for shocks and phase transitions, Arch. Rational Mech. Anal., 83 (1983), pp. 333-361.
    • (1983) Arch. Rational Mech. Anal. , vol.83 , pp. 333-361
    • Hagan, R.1    Slemrod, M.2
  • 18
    • 0030584308 scopus 로고    scopus 로고
    • Global solutions of a high-dimensional system for Korteweg materials
    • H. HATTORI AND D. Li, Global solutions of a high-dimensional system for Korteweg materials, J. Math. Anal. Appl., 198 (1996), pp. 84-97.
    • (1996) J. Math. Anal. Appl. , vol.198 , pp. 84-97
    • Hattori, H.1    Li, D.2
  • 19
    • 0031508127 scopus 로고    scopus 로고
    • Non-classical shocks and kinetic relations: Scalar conservation laws
    • B. HAYES AND P. LEFLOCH, Non-classical shocks and kinetic relations: Scalar conservation laws, Arch. Rational Mech. Anal., 139 (1997), pp. 1-56.
    • (1997) Arch. Rational Mech. Anal. , vol.139 , pp. 1-56
    • Hayes, B.1    Lefloch, P.2
  • 20
    • 22644450850 scopus 로고    scopus 로고
    • Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes
    • 199
    • B. HAYES AND M. SHEARER, Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes, Proc. Roy. Soc. Edinburgh, Sect. A, Math., 129 (199), pp. 733-754.
    • Proc. Roy. Soc. Edinburgh, Sect. A, Math. , vol.129 , pp. 733-754
    • Hayes, B.1    Shearer, M.2
  • 21
    • 0000261039 scopus 로고
    • Travelling wave solutions of the modified Korteweg-de Vries-Burgers equation
    • D. JACOBS, W. MCKINNEY, AND M. SHEARER, Travelling wave solutions of the modified Korteweg-de Vries-Burgers equation, J. Differential Equations, 116 (1995), pp. 448-467.
    • (1995) J. Differential Equations , vol.116 , pp. 448-467
    • Jacobs, D.1    Mckinney, W.2    Shearer, M.3
  • 22
    • 0034482301 scopus 로고    scopus 로고
    • Non-classical kinematic shocks in suspensions of particles in fluids
    • A. KLUWICK, E. COX, AND S. SCHEICHL, Non-classical kinematic shocks in suspensions of particles in fluids, Acta Mech., 144 (2000), pp. 197-210.
    • (2000) Acta Mech. , vol.144 , pp. 197-210
    • Kluwick, A.1    Cox, E.2    Scheichl, S.3
  • 23
    • 0036434955 scopus 로고    scopus 로고
    • Zero diffusion-dispersion limits for scalar conservation laws
    • C. KONDO AND P. LEFLOCH, Zero diffusion-dispersion limits for scalar conservation laws, SIAM J. Math. Anal., 33 (2002), pp. 1320-1329.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1320-1329
    • Kondo, C.1    Lefloch, P.2
  • 24
    • 0000220623 scopus 로고
    • First order quasilinear equations with several independent variables
    • S. KRUZKOV, First order quasilinear equations with several independent variables, Math. USSR-Sb., 123 (1970), pp. 228-255.
    • (1970) Math. USSR-Sb. , vol.123 , pp. 228-255
    • Kruzkov, S.1
  • 25
    • 0037492836 scopus 로고
    • Rigorous treatment of the van der Waals-Maxwell theory of the liquid-vapor transition
    • J. LEBOWITZ AND O. PENROSE, Rigorous treatment of the van der Waals-Maxwell theory of the liquid-vapor transition, J. Math. Phys., 7 (1966), pp. 98-113.
    • (1966) J. Math. Phys. , vol.7 , pp. 98-113
    • Lebowitz, J.1    Penrose, O.2
  • 26
    • 0001819709 scopus 로고    scopus 로고
    • An introduction to nonclassical shocks of systems of conservation laws
    • An Introduction to Recent Developments in Theory and Numerics for Conservation Laws D. Kröner, M. Ohlberger, and C. Rohde eds., Springer-Verlag
    • P. LEFLOCH, An introduction to nonclassical shocks of systems of conservation laws, in An Introduction to Recent Developments in Theory and Numerics for Conservation Laws. D. Kröner, M. Ohlberger, and C. Rohde eds., Lect. Notes Comput. Sci. Engrg. 5, Springer-Verlag, 1999, pp. 28-72.
    • (1999) Lect. Notes Comput. Sci. Engrg. , vol.5 , pp. 28-72
    • Lefloch, P.1
  • 27
    • 2642546433 scopus 로고    scopus 로고
    • Hyperbolic systems of conservation laws. the theory of classical and nonclassical shock waves
    • Birkhauser Verlag, Basel, Switzerland
    • P. LEFLOCH, Hyperbolic systems of conservation laws. The theory of classical and nonclassical shock waves, Lect. Math., Birkhauser Verlag, Basel, Switzerland, 2002.
    • (2002) Lect. Math.
    • Lefloch, P.1
  • 28
    • 0039248884 scopus 로고    scopus 로고
    • Existence theory for the Riemann problem with vanishing diffusion and dispersion
    • P. LEFLOCH AND C. ROHDE, Existence theory for the Riemann problem with vanishing diffusion and dispersion, Indiana Univ. Math. J., 50 (2001), pp. 1707-1743.
    • (2001) Indiana Univ. Math. J. , vol.50 , pp. 1707-1743
    • Lefloch, P.1    Rohde, C.2
  • 29
    • 0001764754 scopus 로고
    • -1,q est compacte pour tout q < 2
    • -1,q est compacte pour tout q < 2, J. Math. Pures Appl., 60 (1981), pp. 309-322.
    • (1981) J. Math. Pures Appl. , vol.60 , pp. 309-322
    • Murat, F.1
  • 30
    • 0034441979 scopus 로고    scopus 로고
    • Finite scale microstructures in nonlocal elasticity
    • X. REN AND L. TRUSKINOVSKY, Finite scale microstructures in nonlocal elasticity, J. Elasticity, 59 (2000), pp. 319-355.
    • (2000) J. Elasticity , vol.59 , pp. 319-355
    • Ren, X.1    Truskinovsky, L.2
  • 31
    • 84858155484 scopus 로고    scopus 로고
    • On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions
    • Math. Institut, Universität Freiburg No. 18, Freiburg, Germany
    • C. ROHDE, On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions, Technical report, Math. Institut, Universität Freiburg No. 18, Freiburg, Germany, 2004.
    • (2004) Technical Report
    • Rohde, C.1
  • 32
    • 0001648070 scopus 로고
    • Convergence of solutions to nonlinear dispersive equations
    • M. SCHONBEK, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations, 7 (1982), pp. 959-1000.
    • (1982) Comm. Partial Differential Equations , vol.7 , pp. 959-1000
    • Schonbek, M.1
  • 34
    • 0020500507 scopus 로고
    • Admissibility criteria for propagating phase boundaries in a van der Waals fluid
    • M. SLEMROD, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81 (1983), pp. 301-315.
    • (1983) Arch. Rational Mech. Anal. , vol.81 , pp. 301-315
    • Slemrod, M.1
  • 35
    • 0001137470 scopus 로고
    • An existence result for scalar conservation laws using measure valued solutions
    • A. SZEPESSY, An existence result for scalar conservation laws using measure valued solutions, Comm. Partial Differential Equations, 14 (1989), pp. 1329-1350.
    • (1989) Comm. Partial Differential Equations , vol.14 , pp. 1329-1350
    • Szepessy, A.1
  • 36
    • 0000553356 scopus 로고
    • Thermodynamische theorie der kapillarität unter voraussetzung stetiger dichteänderung
    • J. VAN DER WAALS, Thermodynamische Theorie der Kapillarität unter Voraussetzung stetiger Dichteänderung, Z. Phys. Chem., 13 (1894), pp. 657-725.
    • (1894) Z. Phys. Chem. , vol.13 , pp. 657-725
    • Van Der Waals, J.1


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