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Volumn 4, Issue 4, 1997, Pages 439-457

Weak solutions to quasilinear wave equations of Klein-Gordon or Sine-Gordon type and relaxation to reaction-diffusion eauations

Author keywords

Compensated compactness; Fractional step method; Klein gordon and sine gordon equation; Lax friedrichs and godunov scheme; Momentum relaxation time; Reaction diffusion equation; Relaxation theory

Indexed keywords


EID: 0002421088     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050024     Document Type: Article
Times cited : (10)

References (28)
  • 1
    • 0002337397 scopus 로고
    • Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics
    • G.Q. CHEN, X. DING, P. LUO, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics, Comm. Math. Phys. 121, 63-84, (1989).
    • (1989) Comm. Math. Phys. , vol.121 , pp. 63-84
    • Chen, G.Q.1    Ding, X.2    Luo, P.3
  • 2
    • 0000805398 scopus 로고
    • Positively invariant regions for systems of non-linear diffusion equations
    • K.N. CHUEH, C.C. CONLEY, J.A. SMOLLER, Positively invariant regions for systems of non-linear diffusion equations, Indiana Univ. Math. J. 26, 372-411, (1977).
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 372-411
    • Chueh, K.N.1    Conley, C.C.2    Smoller, J.A.3
  • 3
    • 0011436212 scopus 로고
    • Admissibility criteria for hyperbolic conservation laws
    • J. G. CONLON, T.-P. LIU, Admissibility criteria for hyperbolic conservation laws, Indiana Univ. Math. J. 30, G41-652, (1981).
    • (1981) Indiana Univ. Math. J. , vol.30
    • Conlon, J.G.1    Liu, T.-P.2
  • 5
    • 0000824680 scopus 로고
    • Hyperbolic systems of balance laws with inhomogeneity and dissipation
    • C.M. DAFERMOS, L. HSIAO, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31, 471-491, (1982).
    • (1982) Indiana Univ. Math. J. , vol.31 , pp. 471-491
    • Dafermos, C.M.1    Hsiao, L.2
  • 6
    • 0020499710 scopus 로고
    • Convergence of approximate solutions to conservation laws
    • R.J. DI PERNA, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82, 27-70, (1983).
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 27-70
    • Di Perna, R.J.1
  • 7
    • 0002578353 scopus 로고
    • Convergence of the viscosity method for isentropic gas dynamics
    • R.J. DI PERNA, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91, 1-30, (1983).
    • (1983) Comm. Math. Phys. , vol.91 , pp. 1-30
    • Di Perna, R.J.1
  • 8
    • 0000935266 scopus 로고
    • Difference method for the numerical computation of discontinuous solutions of equations of hydrodynamics
    • S.K. GODUNOV, Difference method for the numerical computation of discontinuous solutions of equations of hydrodynamics, Mat. Sb. 47, 271-306, (1959).
    • (1959) Mat. Sb. , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 9
    • 0002950929 scopus 로고
    • Shock waves and entropy
    • E.A. Zarantonello, editor, Academic Press
    • P.D. LAX, Shock waves and entropy. In E.A. Zarantonello, editor, Contributions to Nonlinear Functional Analysis, pages 603-634. Academic Press, 1971.
    • (1971) Contributions to Nonlinear Functional Analysis , pp. 603-634
    • Lax, P.D.1
  • 11
    • 0003227104 scopus 로고
    • Perturbations singulières dans les problèmes aux limites et en contrôle optimale
    • Springer-Verlag, Berlin
    • J.L. LIONS, Perturbations singulières dans les problèmes aux limites et en contrôle optimale, In Lectures Notes in Math., volume 323. Springer-Verlag, Berlin, 1984.
    • (1984) Lectures Notes in Math. , vol.323
    • Lions, J.L.1
  • 12
    • 84968497544 scopus 로고
    • The Riemann problem for general 2 × 2 conservation laws
    • T.-P. LIU, The Riemann problem for general 2 × 2 conservation laws, Trans. Amer. Math. Soc. 199, 89-112, (1974).
    • (1974) Trans. Amer. Math. Soc. , vol.199 , pp. 89-112
    • Liu, T.-P.1
  • 13
    • 0016890833 scopus 로고
    • The entropy condition and the admissibility of shocks
    • T.-P. LIU, The entropy condition and the admissibility of shocks, J. Math. Anal. Appl. 53, 78-88, (1976).
    • (1976) J. Math. Anal. Appl. , vol.53 , pp. 78-88
    • Liu, T.-P.1
  • 14
    • 5844312551 scopus 로고
    • Initial boundary value problem for the spherically symmetric motion of isentropic gas
    • T. MAKING, S. TAKENO, Initial boundary value problem for the spherically symmetric motion of isentropic gas, Technical report, 1993.
    • (1993) Technical Report
    • Making, T.1    Takeno, S.2
  • 15
    • 0000039797 scopus 로고
    • The one-dimensional Darcy's law as the limit of a compressible Euler flow
    • P. MARCATI, A. MILANI, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J. Differential Equations 13, 129-147, (1990).
    • (1990) J. Differential Equations , vol.13 , pp. 129-147
    • Marcati, P.1    Milani, A.2
  • 16
    • 0002662053 scopus 로고
    • Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system
    • P. MARCATI, A. MILANI, P. SECCHI, Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system, Manuscripta Math. 60, 49-69, (1988).
    • (1988) Manuscripta Math. , vol.60 , pp. 49-69
    • Marcati, P.1    Milani, A.2    Secchi, P.3
  • 17
    • 5844391084 scopus 로고
    • Global weak entropy solutions to quasilinear wave equations of Klein-Cordon and Sine-Gordon type
    • Istituto per le Applicazioni del Calcolo "M. Picone", C.N.R., Rome
    • P. MARCATI, R. NATALINI, Global weak entropy solutions to quasilinear wave equations of Klein-Cordon and Sine-Gordon type, Technical report, Istituto per le Applicazioni del Calcolo "M. Picone", C.N.R., Rome, 1995.
    • (1995) Technical Report
    • Marcati, P.1    Natalini, R.2
  • 18
    • 21844490167 scopus 로고
    • Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation
    • P. MARCATI, R. NATALINI, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Rational Mech. Anal. 129, 129-145, (1995).
    • (1995) Arch. Rational Mech. Anal. , vol.129 , pp. 129-145
    • Marcati, P.1    Natalini, R.2
  • 19
    • 84971109210 scopus 로고
    • Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem
    • P. MARCATI, R. NATALINI, Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem, Proc. Roy. Soc. Edinburgh 125A, 115-131, (1995).
    • (1995) Proc. Roy. Soc. Edinburgh , vol.125 A , pp. 115-131
    • Marcati, P.1    Natalini, R.2
  • 20
    • 0008949261 scopus 로고    scopus 로고
    • Hyperbolic to parabolic relaxation theory for quasilinear first order systems
    • Dipartimento di Matematica Pura ed Applicata, L'Aquila, preprint
    • P. MARCATI, B. RUBINO, Hyperbolic to parabolic relaxation theory for quasilinear first order systems, Technical report, Dipartimento di Matematica Pura ed Applicata, L'Aquila, 1996. preprint.
    • (1996) Technical Report
    • Marcati, P.1    Rubino, B.2
  • 21
    • 0040695642 scopus 로고    scopus 로고
    • Parabolic relaxation limit for hyperbolic systems of conservation laws
    • P. MARCATI, B. RUBINO, Parabolic relaxation limit for hyperbolic systems of conservation laws, Rend. Circ. Maf. Palermo (2), Suppl. 45, 393-406, (1996).
    • (1996) Rend. Circ. Maf. Palermo (2) , Issue.45 SUPPL. , pp. 393-406
    • Marcati, P.1    Rubino, B.2
  • 22
    • 0001764754 scopus 로고
    • -1,q est compacte pour tout q < 2
    • -1,q est compacte pour tout q < 2, Math. Pures Appl. 60, 309-322, (1981).
    • (1981) Math. Pures Appl. , vol.60 , pp. 309-322
    • Murat, F.1
  • 23
    • 0030584304 scopus 로고    scopus 로고
    • The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations
    • R. NATALINI, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations, J. Math. Anal. Appl. 198, 262-281, (1996).
    • (1996) J. Math. Anal. Appl. , vol.198 , pp. 262-281
    • Natalini, R.1
  • 24
    • 0029715273 scopus 로고    scopus 로고
    • Convergence of the fractional step method for a 2 × 2 nonstrictly hyperbolic system of conservation laws
    • B. RUBINO, Convergence of the fractional step method for a 2 × 2 nonstrictly hyperbolic system of conservation laws, J. Math. Anal. Appl. 197, 286-317 (1996).
    • (1996) J. Math. Anal. Appl. , vol.197 , pp. 286-317
    • Rubino, B.1
  • 25
    • 0002609873 scopus 로고    scopus 로고
    • Porous media flow as the limit of a nonstrictly hyperbolic system of conservation laws
    • B. RUBINO, Porous media flow as the limit of a nonstrictly hyperbolic system of conservation laws, Comm. Partial Differential Equations 21, 1-21 (1996).
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 1-21
    • Rubino, B.1
  • 27
    • 0002851015 scopus 로고
    • The compensated compactness method applied to partial differential equations
    • J.M.Ball, editor, Reidel, Dordrecht, NATO ASI
    • L. TARTAR, The compensated compactness method applied to partial differential equations, In J.M.Ball, editor, Systems of Nonlinear Partial Differential Equations, Reidel, Dordrecht, 1983. NATO ASI.
    • (1983) Systems of Nonlinear Partial Differential Equations
    • Tartar, L.1
  • 28
    • 84980140114 scopus 로고
    • Global solutions of the Cauchy problem for a nonhomogeneous quasilinear hyperbolic system
    • L. YING, G. WANG, Global solutions of the Cauchy problem for a nonhomogeneous quasilinear hyperbolic system, Comm. Pure and Appl. Math. 33, 579-597, (1980).
    • (1980) Comm. Pure and Appl. Math. , vol.33 , pp. 579-597
    • Ying, L.1    Wang, G.2


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