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Volumn 70, Issue 1-2, 1998, Pages 175-193

Global existence and optimal temporal decay estimates for systems of parabolic conservation laws I: The one-dimensional case

Author keywords

Entropy entropy flux pairs; Global existence; Nonlinear parabolic conservation laws; Optimal decay estimates; Sobolev imbedding theorems

Indexed keywords


EID: 0011469049     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036819808840683     Document Type: Article
Times cited : (9)

References (24)
  • 1
    • 0000170201 scopus 로고
    • Multiple—mode diffusion waves for viscous nonstrictly hyperbolic conservation laws
    • Chen, I-Liang. 1991. Multiple—mode diffusion waves for viscous nonstrictly hyperbolic conservation laws. Comm. Math. Phys, 138: 51-61.
    • (1991) Comm. Math. Phys , vol.138 , pp. 51-61
    • Chen, I.-L.1
  • 2
    • 0039657693 scopus 로고
    • Taiping Liu, Convergence to diffusion waves of solutions for viscous conservation laws
    • Erratum, Comm. Math. Phys., 120(1987), 525-527
    • Chen, I-Liang. 1987. Taiping Liu, Convergence to diffusion waves of solutions for viscous conservation laws. Comm. Math. Phys, 110: 503-517. Erratum, Comm. Math. Phys., 120(1987), 525-527
    • (1987) Comm. Math. Phys , vol.110 , pp. 503-517
    • Chen, I.-L.1
  • 4
    • 0001715095 scopus 로고
    • Estimates for conservation laws with little viscosity
    • Dafermos, C.M., 1987. Estimates for conservation laws with little viscosity. SIAM Journal on Mathematical Analysis, 18: 409-421.
    • (1987) SIAM Journal on Mathematical Analysis , vol.18 , pp. 409-421
    • Dafermos, C.M.1
  • 5
  • 6
    • 8744314304 scopus 로고
    • Global solution of a semilinear parabolic system
    • Ding, X.X., and Zhao, H.J., 1991. Global solution of a semilinear parabolic system. Acta Mathematica Scientia, 11: 254-266.
    • (1991) Acta Mathematica Scientia , vol.11 , pp. 254-266
    • Ding, X.X.1    Zhao, H.J.2
  • 8
    • 85050699618 scopus 로고
    • Solutions in the large for certain nonlinear parabolic sys- tems
    • Hoff, D., and Smoller, J.A., 1985. Solutions in the large for certain nonlinear parabolic sys- tems. Analyse Nonlineaire, 2: 213-235.
    • (1985) Analyse Nonlineaire , vol.2 , pp. 213-235
    • Hoff, D.1    Smoller, J.A.2
  • 9
    • 0003180894 scopus 로고
    • Global existence for systems of parabolic conservation laws
    • Hoff, D., and Smoller, J.A., 1987. Global existence for systems of parabolic conservation laws. Journal of Differential Equations, 68: 210-220.
    • (1987) Journal of Differential Equations , vol.68 , pp. 210-220
    • Hoff, D.1    Smoller, J.A.2
  • 10
    • 84912583141 scopus 로고
    • On the Cauchy problem for the system of fundamental equations describing the movement of a compressible fluid
    • Itaya, N., 1971. On the Cauchy problem for the system of fundamental equations describing the movement of a compressible fluid. Kadai Math. Sem. Rep, 23: 60-120.
    • (1971) Kadai Math. Sem. Rep , vol.23 , pp. 60-120
    • Itaya, N.1
  • 11
    • 49949145725 scopus 로고
    • On some systems of quasilinear parabolic equations
    • Kanel, Y., 1966. On some systems of quasilinear parabolic equations. USSR Comp. Math.and Math. Phys, 6: 74-88.
    • (1966) USSR Comp. Math.and Math. Phys , vol.6 , pp. 74-88
    • Kanel, Y.1
  • 12
    • 0000416468 scopus 로고
    • On a model system of equations of one-dimensional gas motion
    • Kanel, Y., 1968. On a model system of equations of one-dimensional gas motion. Diff. Equs, 4: 374-386.
    • (1968) Diff. Equs , vol.4 , pp. 374-386
    • Kanel, Y.1
  • 14
    • 85065362210 scopus 로고
    • Unique global solution in time of initial-boundary-value problem for one-dimensional equations of a viscous gas
    • Kazhikov, A., and Shelukhin, V., 1977. Unique global solution in time of initial-boundary-value problem for one-dimensional equations of a viscous gas. P.M.M.J.App1. Math.Mech, 49: 273-281.
    • (1977) P.M.M.J.App1. Math.Mech , vol.49 , pp. 273-281
    • Kazhikov, A.1    Shelukhin, V.2
  • 15
    • 0002321065 scopus 로고
    • The initial-value problem for the equations of motion of viscous and heat conductive gases
    • Matsumura, A., and Nishida, T., 1980. The initial-value problem for the equations of motion of viscous and heat conductive gases. J.Math.Kyoto Univ, 20: 67-104.
    • (1980) J.Math.Kyoto Univ , vol.20 , pp. 67-104
    • Matsumura, A.1    Nishida, T.2
  • 16
    • 84990619724 scopus 로고
    • A class of convergent finite-difference schemes for certain nonlinear parabolic systems
    • Nishida, T., and Smoiler, J.A., 1983. A class of convergent finite-difference schemes for certain nonlinear parabolic systems. Communications on Pure and Applied Mathematics, 36: 785-808.
    • (1983) Communications on Pure and Applied Mathematics , vol.36 , pp. 785-808
    • Nishida, T.1    Smoiler, J.A.2
  • 18
    • 0000999183 scopus 로고
    • Uniform decay rate for parabolic conservation laws
    • Schonbek, M., 1986. Uniform decay rate for parabolic conservation laws. Nonlinear Anal- ysis, TMA, 10 (9): 943-956.
    • (1986) Nonlinear Anal- ysis, TMA , vol.10 , Issue.9 , pp. 943-956
    • Schonbek, M.1
  • 20
    • 84968480726 scopus 로고
    • Lower bounds of rates of decay for solutions to the Navier-Stokes equations
    • Schonbek, M., 1991. Lower bounds of rates of decay for solutions to the Navier-Stokes equations. Journal of American Mathematical Socirty, 4 (1-2): 423-440.
    • (1991) Journal of American Mathematical Socirty , vol.4 , Issue.1-2 , pp. 423-440
    • Schonbek, M.1
  • 21
    • 21344449035 scopus 로고    scopus 로고
    • On the decay of higher order norms of solutions of Navier-Stokes equations
    • Schonbek, M., and Wiegner, M., 1996. On the decay of higher order norms of solutions of Navier-Stokes equations. Proceedings of the Royal Society of Edinburgh, 126A (1-2): 677-685.
    • (1996) Proceedings of the Royal Society of Edinburgh , vol.126A , Issue.1-2 , pp. 677-685
    • Schonbek, M.1    Wiegner, M.2
  • 22
  • 23
    • 51249183619 scopus 로고
    • Existence and nonexistence of global solutions for a semilinear heat
    • Weissler, F.B., 1981. Existence and nonexistence of global solutions for a semilinear heat. Israel Journal of Mathematics, 38 (1-2): 29-40.
    • (1981) Israel Journal of Mathematics , vol.38 , Issue.1-2 , pp. 29-40
    • Weissler, F.B.1
  • 24
    • 0011487864 scopus 로고
    • Solutions in the large for certain nonlinear parabolic systems in arbitrary spatial dimensions
    • Zhao, H.J., 1981. Solutions in the large for certain nonlinear parabolic systems in arbitrary spatial dimensions. Applicable Analysis, 59 (1-2): 349-376.
    • (1981) Applicable Analysis , vol.59 , Issue.1-2 , pp. 349-376
    • Zhao, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.