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Volumn 61, Issue 2, 2003, Pages 295-313

Asymptotic behavior of solutions to quasilinear hyperbolic equations with nonlinear damping

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; HEAT FLUX; LINEAR EQUATIONS; ONE DIMENSIONAL; PROBLEM SOLVING; TEMPERATURE; THEOREM PROVING;

EID: 0038278399     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1976371     Document Type: Article
Times cited : (21)

References (30)
  • 1
    • 0001558282 scopus 로고
    • Implication of a nonlinearity in the theory of second sound in solids
    • Coleman, B. D., and Neumann, D. C., Implication of a nonlinearity in the theory of second sound in solids, Phys. Rev. B 32, 1492-1498 (1988)
    • (1988) Phys. Rev. B , vol.32 , pp. 1492-1498
    • Coleman, B.D.1    Neumann, D.C.2
  • 2
    • 0000439094 scopus 로고
    • A system of hyperbolic conservation laws with frictional damping
    • Dafermos, C. M. A system of hyperbolic conservation laws with frictional damping, Z. Angew. Math. Phys. 46 Special Issue, 294-307 (1995)
    • (1995) Z. Angew. Math. Phys. , vol.46 , Issue.SPEC. ISSUE , pp. 294-307
    • Dafermos, C.M.1
  • 3
    • 0003660460 scopus 로고    scopus 로고
    • Quasilinear hyperbolic system and dissipative mechanisms
    • World Scientific, Singapore
    • Hsiao, L., "Quasilinear Hyperbolic System and Dissipative Mechanisms", World Scientific, Singapore, 1997.
    • (1997)
    • Hsiao, L.1
  • 4
    • 0000580833 scopus 로고
    • Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
    • Hsiao, L. and Liu, T.-P., Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping, Comm. Math. Phys. 143, 599-605 (1992)
    • (1992) Comm. Math. Phys. , vol.143 , pp. 599-605
    • Hsiao, L.1    Liu, T.-P.2
  • 5
    • 0001647791 scopus 로고
    • Nonlinear diffusive phenomena of nonlinear hyperbolic systems
    • Hsiao, L., and Liu, T.-P., Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chin. Ann. of Math. 14B, 465-480 (1993)
    • (1993) Chin. Ann. of Math. , vol.14 B , pp. 465-480
    • Hsiao, L.1    Liu, T.-P.2
  • 6
    • 0030096163 scopus 로고    scopus 로고
    • Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media
    • Hsiao, L., and Luo, T., Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. Differential Equations 125, 329-365 (1996)
    • (1996) J. Differential Equations , vol.125 , pp. 329-365
    • Hsiao, L.1    Luo, T.2
  • 7
    • 0032027394 scopus 로고    scopus 로고
    • Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping
    • Hsiao, L., and Luo, T., Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping, Quart. Appl. Math. 56, 173-198 (1998)
    • (1998) Quart. Appl. Math. , vol.56 , pp. 173-198
    • Hsiao, L.1    Luo, T.2
  • 8
    • 0033589577 scopus 로고    scopus 로고
    • Initial boundary value problem for the system of compressible adiabatic flow through porous media
    • Hsiao, L., and Pan, P. H., Initial boundary value problem for the system of compressible adiabatic flow through porous media, J. Differential Equations 159, 280-305 (1999)
    • (1999) J. Differential Equations , vol.159 , pp. 280-305
    • Hsiao, L.1    Pan, P.H.2
  • 9
    • 0030544338 scopus 로고    scopus 로고
    • Global existence of solutions for the system of compressible adiabatic flow through porous media
    • Hsiao, L., and Serre, D., Global existence of solutions for the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal. 27, 70-77 (1996)
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 70-77
    • Hsiao, L.1    Serre, D.2
  • 10
    • 21844509114 scopus 로고
    • Large-time behavior of solutions for the system of compressible adiabatic flow through porous media
    • Hsiao, L., and Serre, D., Large-time behavior of solutions for the system of compressible adiabatic flow through porous media, Chin. Ann. of Math. 16B, 431-444 (1995)
    • (1995) Chin. Ann. of Math. , vol.16 B , pp. 431-444
    • Hsiao, L.1    Serre, D.2
  • 11
    • 0029111297 scopus 로고
    • Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping
    • Hsiao, L., and Tang, S. Q., Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping, Quart. Appl. Math. LIII, 487-505 (1995)
    • (1995) Quart. Appl. Math. , vol.53 , pp. 487-505
    • Hsiao, L.1    Tang, S.Q.2
  • 12
    • 0001134867 scopus 로고
    • Construction and qualitative behavior of solutions of perturbated Riemann problem for the system of one-dimensional isentropic flow with damping
    • Hsiao, L., and Tang, S. Q., Construction and qualitative behavior of solutions of perturbated Riemann problem for the system of one-dimensional isentropic flow with damping, J. Differential Equations 123, 480-503 (1995)
    • (1995) J. Differential Equations , vol.123 , pp. 480-503
    • Hsiao, L.1    Tang, S.Q.2
  • 13
    • 0005618903 scopus 로고    scopus 로고
    • The asymptotic behavior of solutions to the damped p-system with boundary effects
    • Li, H. L., The asymptotic behavior of solutions to the damped p-system with boundary effects, J. Partial Diff. Eqns. 12, 357-368 (1999)
    • (1999) J. Partial Diff. Eqns. , vol.12 , pp. 357-368
    • Li, H.L.1
  • 14
    • 0003656444 scopus 로고
    • Boundary value problem for quasilinear hyperbolic systems
    • Duke Univ. Math. Ser. V
    • Li, T. T., and Yu, W. C., Boundary value problem for quasilinear hyperbolic systems, Duke Univ. Math. Ser. V 1985.
    • (1985)
    • Li, T.T.1    Yu, W.C.2
  • 15
    • 85039660079 scopus 로고    scopus 로고
    • The interaction of elementary waves for the isentropic Euler equation with frictional damping
    • preprint
    • Luo, T., and Yang, T., The interaction of elementary waves for the isentropic Euler equation with frictional damping, preprint.
    • Luo, T.1    Yang, T.2
  • 16
    • 4243244646 scopus 로고    scopus 로고
    • Global existence of weak entropy solutions for damped p-system
    • to appear
    • Luo, T., and Yang, T., Global existence of weak entropy solutions for damped p-system, to appear.
    • Luo, T.1    Yang, T.2
  • 17
    • 0003839761 scopus 로고    scopus 로고
    • Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping
    • preprint
    • Marcati, P., and Mei, M., Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping, preprint 1998
    • (1998)
    • Marcati, P.1    Mei, M.2
  • 18
    • 0011400198 scopus 로고
    • Nonlinear hyperbolic equations and related topics in fluid dynamics
    • Publications Mathematiques D'Orsay, 78.02, Dept. de mathematique, Paris-Sud
    • Nishida, T., Nonlinear hyperbolic equations and related topics in fluid dynamics, Publications Mathematiques D'Orsay, 78.02, Dept. de mathematique, Paris-Sud (1978)
    • (1978)
    • Nishida, T.1
  • 19
    • 0030295223 scopus 로고    scopus 로고
    • Convergence rates to nonlinear diffusion waves for solutions of systems of hyperbolic conservation laws with damping
    • Nishihara, K., Convergence rates to nonlinear diffusion waves for solutions of systems of hyperbolic conservation laws with damping, J. Differential Equations 131, 171-188 (1996)
    • (1996) J. Differential Equations , vol.131 , pp. 171-188
    • Nishihara, K.1
  • 20
    • 0001092706 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
    • Nishihara, K., Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping, J. Differential Equations 137, 384-395 (1997)
    • (1997) J. Differential Equations , vol.137 , pp. 384-395
    • Nishihara, K.1
  • 21
    • 0033543057 scopus 로고    scopus 로고
    • Boundary effect on asymptotic behavior of solutions to the P-system with damping
    • Nishihara, K., and Yang, T., Boundary effect on asymptotic behavior of solutions to the P-system with damping, J. Differential Equations 156 (2), 439-458 (1999)
    • (1999) J. Differential Equations , vol.156 , Issue.2 , pp. 439-458
    • Nishihara, K.1    Yang, T.2
  • 22
    • 0034628139 scopus 로고    scopus 로고
    • p-convergence rate to nonlinear diffusion waves for p-system with damping
    • p-convergence rate to nonlinear diffusion waves for p-system with damping, J. Differential Equations 161, 191-218 (2000)
    • (2000) J. Differential Equations , vol.161 , pp. 191-218
    • Nishihara, K.1    Wang, W.K.2    Yang, T.3
  • 23
    • 0033327924 scopus 로고    scopus 로고
    • On second sound at the critical temperature
    • Saxton, K., Saxton, R., and Kosinski, W., On second sound at the critical temperature, Quart. Appl. Math. 57, 723-740 (1999)
    • (1999) Quart. Appl. Math. , vol.57 , pp. 723-740
    • Saxton, K.1    Saxton, R.2    Kosinski, W.3
  • 24
    • 0037783653 scopus 로고    scopus 로고
    • Nonlinearity and memory effects in low temperature heat propagation
    • Saxton, K., and Saxton, R., Nonlinearity and memory effects in low temperature heat propagation, Arch. Mech. 52, 127-142 (2000)
    • (2000) Arch. Mech. , vol.52 , pp. 127-142
    • Saxton, K.1    Saxton, R.2
  • 25
    • 0001561727 scopus 로고    scopus 로고
    • Asymptotic behavior of large weak entropy solutions of the damped p-system
    • Serre, D., and Xiao, L., Asymptotic behavior of large weak entropy solutions of the damped p-system, J. Partial Diff. Eqns. 10, 355-368 (1997)
    • (1997) J. Partial Diff. Eqns. , vol.10 , pp. 355-368
    • Serre, D.1    Xiao, L.2
  • 26
    • 0019664632 scopus 로고
    • Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
    • Slemrod, M., Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal. 76, 97-133 (1981)
    • (1981) Arch. Rat. Mech. Anal. , vol.76 , pp. 97-133
    • Slemrod, M.1
  • 27
    • 0001421035 scopus 로고
    • A class of similarity solutions of the nonlinear diffusion equation
    • Van Duyn, C. J., and Peletier, L. A., A class of similarity solutions of the nonlinear diffusion equation, Nonlinear Anal., T.M.A., 1, 223-233 (1977)
    • (1977) Nonlinear Anal., T.M.A. , vol.1 , pp. 223-233
    • Van Duyn, C.J.1    Peletier, L.A.2
  • 28
    • 0007088738 scopus 로고
    • Global regularity and formation of singularities of solution for quasilinear hyperbolic system with dissipation
    • Wang, J.-H., and Li, C. Z., Global regularity and formation of singularities of solution for quasilinear hyperbolic system with dissipation, Chinese Annals Math. 9A, 509-523 (1988)
    • (1988) Chinese Annals Math. , vol.9 A , pp. 509-523
    • Wang, J.-H.1    Li, C.Z.2
  • 29
    • 21944446265 scopus 로고    scopus 로고
    • Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms
    • Yang, T., Zhu C., and Zhao, H., Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms. Proc. Roy. Soc. Edin. 127A, 1311-1324 (1997)
    • (1997) Proc. Roy. Soc. Edin. , vol.127 A , pp. 1311-1324
    • Yang, T.1    Zhu, C.2    Zhao, H.3
  • 30
    • 0038460488 scopus 로고    scopus 로고
    • Convergence to strong nonlinear diffusion waves for solutions of p-system with damping
    • submitted
    • Zhao, H., Convergence to strong nonlinear diffusion waves for solutions of p-system with damping J. Differential Equations, submitted.
    • J. Differential Equations
    • Zhao, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.