메뉴 건너뛰기




Volumn 176, Issue 1, 2005, Pages 1-24

Convergence to the barenblatt solution for the compressible euler equations with damping and vacuum

Author keywords

[No Author keywords available]

Indexed keywords


EID: 17444396696     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-004-0349-y     Document Type: Article
Times cited : (151)

References (38)
  • 1
    • 0002293879 scopus 로고
    • The porous media equations
    • Lecture Notes in Math., (A. FASANO, M. PRIMICERIO, Eds) Springer-Verlag, Berlin
    • D.G. ARONSON: The porous media equations. In: "Nonlinear Diffusion Problem", Lecture Notes in Math., Vol. 1224(A. FASANO, M. PRIMICERIO, Eds) Springer-Verlag, Berlin, 1986
    • (1986) Nonlinear Diffusion Problem , vol.1224
    • Aronson, D.G.1
  • 3
    • 0033450362 scopus 로고    scopus 로고
    • Divergence-measure fields and hyperbolic conservation laws
    • G. CHEN, H. FRID: Divergence-measure fields and hyperbolic conservation laws. Arch. Ration. Mech. Anal. 147, 89-118 (1999)
    • (1999) Arch. Ration. Mech. Anal. , vol.147 , pp. 89-118
    • Chen, G.1    Frid, H.2
  • 4
    • 0000805398 scopus 로고
    • Positively invariant regions for systems of nonlinear diffusion equations
    • K. CHUEH, C. CONLEY, J. SMOLLER: Positively invariant regions for systems of nonlinear diffusion equations. Indiana U. Math. J. 26, 373-392 (1977)
    • (1977) Indiana U. Math. J. , vol.26 , pp. 373-392
    • Chueh, K.1    Conley, C.2    Smoller, J.3
  • 5
    • 0018678304 scopus 로고
    • The second law of thermodynamics and stability
    • C.M. DAFERMOS: The second law of thermodynamics and stability. Arch. Ration. Mech. Anal. 70, 167-179 (1979)
    • (1979) Arch. Ration. Mech. Anal. , vol.70 , pp. 167-179
    • Dafermos, C.M.1
  • 6
    • 0000439094 scopus 로고
    • A system of hyperbolic conservation laws with frictional damping
    • C.M. DAFERMOS: 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
  • 8
    • 0002337397 scopus 로고
    • Convergence of the fractional step Lax-Friedrichs and Godunov scheme for isentropic system of gas dynamics
    • X. DING, G. CHEN, P. Luo: Convergence of the fractional step Lax-Friedrichs and Godunov scheme for isentropic system of gas dynamics. Commun. Math. Phys 121, 63-84 (1989)
    • (1989) Commun. Math. Phys , vol.121 , pp. 63-84
    • Ding, X.1    Chen, G.2    Luo, P.3
  • 9
    • 0000408106 scopus 로고
    • Uniqueness of solutions to hyperbolic conservation laws
    • R. DIPERNA: Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ. Math. J. 28, 137-188 (1979)
    • (1979) Indiana Univ. Math. J. , vol.28 , pp. 137-188
    • Diperna, R.1
  • 10
    • 0001421035 scopus 로고
    • A class of similary solutions of the nonlinear diffusion equations
    • C.J. VAN DUYN, L.A. PELETIER: A class of similary solutions of the nonlinear diffusion equations. Nonlinear Analysis, TMA 1, 223-233 (1977)
    • (1977) Nonlinear Analysis, TMA , vol.1 , pp. 223-233
    • Van Duyn, C.J.1    Peletier, L.A.2
  • 12
    • 0000580833 scopus 로고
    • Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
    • L. HSIAO, T. LIU: 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.2
  • 13
    • 0001647791 scopus 로고
    • Nonlinear diffusive phenomena of nonlinear hyperbolic systems
    • L. HSIAO, T. LIU: Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Chin. Ann. of Math. Ser. B 14, 465-480 (1993)
    • (1993) Chin. Ann. of Math. Ser. B , vol.14 , pp. 465-480
    • Hsiao, L.1    Liu, T.2
  • 14
    • 0032027394 scopus 로고    scopus 로고
    • Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping
    • L. HSIAO, T. LUO: Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping. Q. Appl. Math. 56, 173-198 (1998)
    • (1998) Q. Appl. Math. , vol.56 , pp. 173-198
    • Hsiao, L.1    Luo, T.2
  • 15
    • 0007505885 scopus 로고    scopus 로고
    • The damped p-system with boundary effects
    • L. HSIAO, R. PAN: The damped p-system with boundary effects. Contemporary Mathematics 255, 109-123 (2000)
    • (2000) Contemporary Mathematics , vol.255 , pp. 109-123
    • Hsiao, L.1    Pan, R.2
  • 16
    • 0029111297 scopus 로고
    • Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping
    • L. HSIAO, S. TANG: Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping. Q. Appl. Math. 53, 487-505 (1995)
    • (1995) Q. Appl. Math. , vol.53 , pp. 487-505
    • Hsiao, L.1    Tang, S.2
  • 17
    • 0001134867 scopus 로고
    • Construction and qualitative behavior of solutions of perturbated Riemann problem for the system of one-dimensional isentropic flow with damping
    • L. HSIAO, S. TANG: 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.2
  • 19
    • 0037934303 scopus 로고    scopus 로고
    • Convergence rate for compressible Euler equations with damping and vacuum
    • F. HUANG, R. PAN: Convergence rate for compressible Euler equations with damping and vacuum. Arch. Ration. Mech. Anal. 166, 359-376 (2003)
    • (2003) Arch. Ration. Mech. Anal. , vol.166 , pp. 359-376
    • Huang, F.1    Pan, R.2
  • 21
    • 49349118298 scopus 로고
    • Source-type solutions for equations of nonstationary filtration
    • S. KAMIN: Source-type solutions for equations of nonstationary filtration. J. Math. Anal. Appl. 64, 263-276 (1978)
    • (1978) J. Math. Anal. Appl. , vol.64 , pp. 263-276
    • Kamin, S.1
  • 22
    • 0002680118 scopus 로고    scopus 로고
    • Compressible flow with damping and vacuum
    • T. Liu: Compressible flow with damping and vacuum. Japan J. Appl. Math 13, 25-32 (1996)
    • (1996) Japan J. Appl. Math , vol.13 , pp. 25-32
    • Liu, T.1
  • 23
    • 84990578229 scopus 로고
    • The existence of a global weak solution to the nonlinear water-hammar problem
    • M. LUSKIN, B. TEMPLE: The existence of a global weak solution to the nonlinear water-hammar problem. Comm. Pure Appl. Math. 35 697-735 (1982)
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 697-735
    • Luskin, M.1    Temple, B.2
  • 24
    • 0001736387 scopus 로고    scopus 로고
    • Compressible Euler equations with vacuum
    • T. Liu, T. YANG: Compressible Euler equations with vacuum. J. Differential Equations 140, 223-237 (1997)
    • (1997) J. Differential Equations , vol.140 , pp. 223-237
    • Liu, T.1    Yang, T.2
  • 26
    • 85047696623 scopus 로고    scopus 로고
    • Interaction of elementary waves for compressible Euler equations with frictional damping
    • T. Luo, T. YANG: Interaction of elementary waves for compressible Euler equations with frictional damping. J. Differential Equations 161, 42-86 (2000)
    • (2000) J. Differential Equations , vol.161 , pp. 42-86
    • Luo, T.1    Yang, T.2
  • 27
    • 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 84, 129-147 (1990)
    • (1990) J. Differential Equations , vol.84 , pp. 129-147
    • Marcati, P.1    Milani, A.2
  • 28
    • 0034629684 scopus 로고    scopus 로고
    • Hyperbolic to parabolic relaxation theory for quasilinear first order systems
    • P. MARCATI, B. RUBINO: Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems. J. Differential Equations 162, 359-399 (2000)
    • (2000) J. Differential Equations , vol.162 , pp. 359-399
    • Marcati, P.1    Rubino, B.2
  • 29
    • 0011400198 scopus 로고
    • Nonlinear hyperbolic equations and related topics in fluid dynamics
    • T. NISHIDA: Nonlinear hyperbolic equations and related topics in fluid dynamics. Publ. Math. D'Orsay 46-53 (1978)
    • (1978) Publ. Math. D'Orsay , pp. 46-53
    • Nishida, T.1
  • 30
    • 0030295223 scopus 로고    scopus 로고
    • Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping
    • K. NISHIHARA: Convergence rates to nonlinear diffusion waves for solutions of system 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
  • 31
    • 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.2    Yang, T.3
  • 32
    • 0033543057 scopus 로고    scopus 로고
    • Boundary effect on asymptotic behavior of solutions to the p-system with damping
    • K. NISHIHARA, T. YANG: Boundary effect on asymptotic behavior of solutions to the p-system with damping. J. Differential Equations 156, 439-458 (1999)
    • (1999) J. Differential Equations , vol.156 , pp. 439-458
    • Nishihara, K.1    Yang, T.2
  • 34
    • 0001561727 scopus 로고    scopus 로고
    • Asymptotic behavior of large weak entropy solutions of the damped p-system
    • D. SERRE, L. XIAO: Asymptotic behavior of large weak entropy solutions of the damped p-system. J. P. Diff. Equa. 10, 355-368 (1997)
    • (1997) J. P. Diff. Equa. , vol.10 , pp. 355-368
    • Serre, D.1    Xiao, L.2
  • 36
    • 0035920063 scopus 로고    scopus 로고
    • Convergence to strong nonlinear diffusion waves for solutions of p-system with damping
    • H. ZHAO: Convergence to strong nonlinear diffusion waves for solutions of p-system with damping. J. Differential Equations 174, 200-236 (2001)
    • (2001) J. Differential Equations , vol.174 , pp. 200-236
    • Zhao, H.1
  • 37
    • 0001097191 scopus 로고    scopus 로고
    • Global smooth solutions to the adiabatic gas dynamics system with dissipation terms
    • Y. ZHENG: Global smooth solutions to the adiabatic gas dynamics system with dissipation terms. Chinese Ann. of Math. Ser. A 17, 155-162 (1996)
    • (1996) Chinese Ann. of Math. Ser. A , vol.17 , pp. 155-162
    • Zheng, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.