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Hyperbolic balance laws with relaxation
1. | Division of Applied Mathematics, Brown University, Providence, RI 02912, United States |
References:
[1] |
D. Amadori and G. Guerra, Uniqueness and continuous dependence for systems of balance laws with dissipation,, Nonlinear Anal., 49 (2002), 987.
doi: 10.1016/S0362-546X(01)00721-0. |
[2] |
S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems,, Ann.of Math., 161 (2005), 223.
doi: 10.4007/annals.2005.161.223. |
[3] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, Comm. Pure Appl. Math., 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[4] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,, Oxford Lecture Series in Mathematics and its Applications, (2000).
|
[5] |
C. C. Christoforou, Hyperbolic systems of balance laws via vanishing viscosity,, J. Differential Equations, 221 (2006), 470.
doi: 10.1016/j.jde.2005.03.010. |
[6] |
C. M. Dafermos, Hyperbolic systems of balance laws with weak dissipation,, J. Hyperbolic Differ. Equ., 3 (2006), 507.
doi: 10.1142/S0219891606000884. |
[7] |
C. M. Dafermos, BV solutions for hyperbolic systems of balance laws with relaxation,, J. Differential Equations, 255 (2013), 2521.
doi: 10.1016/j.jde.2013.07.002. |
[8] |
C. M. Dafermos, Redistribution of damping in viscoelasticity,, Comm. Partial Differential Equations, 38 (2013), 1274.
doi: 10.1080/03605302.2012.755544. |
[9] |
C. M. Dafermos, Heat flow with shocks in media with memory,, Indiana U. Math. J., 62 (2013), 1443.
doi: 10.1512/iumj.2013.62.5126. |
[10] |
C. M. Dafermos, Asymptotic behavior of BV solutions to the equations of nonlinear viscoelasticity,, Commun. Inf. Syst., 13 (2013), 201.
doi: 10.4310/CIS.2013.v13.n2.a4. |
[11] |
C. M. Dafermos, BV solutions of hyperbolic balance laws with relaxation in the absence of conserved quantities,, SIAM J. Math. Analysis, 46 (2014), 4014.
doi: 10.1137/14096075X. |
[12] |
C. M. Dafermos, Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation,, J. Hyperbolic Differ. Equ., 12 (2015), 277.
doi: 10.1142/S0219891615500083. |
[13] |
C. M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation,, Indiana Univ. Math. J., 31 (1982), 471.
doi: 10.1512/iumj.1982.31.31039. |
[14] |
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations,, Comm. Pure Appl. Math., 18 (1965), 697.
doi: 10.1002/cpa.3160180408. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws,, Comm. Pure Appl. Math., 10 (1957), 537.
doi: 10.1002/cpa.3160100406. |
[16] |
T.-P. Liu, Admissible solutions of hyperbolic conservation laws,, Memoirs AMS, 30 (1981).
doi: 10.1090/memo/0240. |
[17] |
T. Ruggeri and D. Serre, Stability of constant equilibrium state for dissipative balance laws systems with a convex entropy,, Quart. Appl. Math., 62 (2004), 163.
|
[18] |
H. Zeng, A class of initial value problems for $2\times 2$ hyperbolic systems with relaxation,, J. Differential Equations, 251 (2011), 1254.
doi: 10.1016/j.jde.2011.05.018. |
show all references
References:
[1] |
D. Amadori and G. Guerra, Uniqueness and continuous dependence for systems of balance laws with dissipation,, Nonlinear Anal., 49 (2002), 987.
doi: 10.1016/S0362-546X(01)00721-0. |
[2] |
S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems,, Ann.of Math., 161 (2005), 223.
doi: 10.4007/annals.2005.161.223. |
[3] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, Comm. Pure Appl. Math., 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[4] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,, Oxford Lecture Series in Mathematics and its Applications, (2000).
|
[5] |
C. C. Christoforou, Hyperbolic systems of balance laws via vanishing viscosity,, J. Differential Equations, 221 (2006), 470.
doi: 10.1016/j.jde.2005.03.010. |
[6] |
C. M. Dafermos, Hyperbolic systems of balance laws with weak dissipation,, J. Hyperbolic Differ. Equ., 3 (2006), 507.
doi: 10.1142/S0219891606000884. |
[7] |
C. M. Dafermos, BV solutions for hyperbolic systems of balance laws with relaxation,, J. Differential Equations, 255 (2013), 2521.
doi: 10.1016/j.jde.2013.07.002. |
[8] |
C. M. Dafermos, Redistribution of damping in viscoelasticity,, Comm. Partial Differential Equations, 38 (2013), 1274.
doi: 10.1080/03605302.2012.755544. |
[9] |
C. M. Dafermos, Heat flow with shocks in media with memory,, Indiana U. Math. J., 62 (2013), 1443.
doi: 10.1512/iumj.2013.62.5126. |
[10] |
C. M. Dafermos, Asymptotic behavior of BV solutions to the equations of nonlinear viscoelasticity,, Commun. Inf. Syst., 13 (2013), 201.
doi: 10.4310/CIS.2013.v13.n2.a4. |
[11] |
C. M. Dafermos, BV solutions of hyperbolic balance laws with relaxation in the absence of conserved quantities,, SIAM J. Math. Analysis, 46 (2014), 4014.
doi: 10.1137/14096075X. |
[12] |
C. M. Dafermos, Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation,, J. Hyperbolic Differ. Equ., 12 (2015), 277.
doi: 10.1142/S0219891615500083. |
[13] |
C. M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation,, Indiana Univ. Math. J., 31 (1982), 471.
doi: 10.1512/iumj.1982.31.31039. |
[14] |
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations,, Comm. Pure Appl. Math., 18 (1965), 697.
doi: 10.1002/cpa.3160180408. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws,, Comm. Pure Appl. Math., 10 (1957), 537.
doi: 10.1002/cpa.3160100406. |
[16] |
T.-P. Liu, Admissible solutions of hyperbolic conservation laws,, Memoirs AMS, 30 (1981).
doi: 10.1090/memo/0240. |
[17] |
T. Ruggeri and D. Serre, Stability of constant equilibrium state for dissipative balance laws systems with a convex entropy,, Quart. Appl. Math., 62 (2004), 163.
|
[18] |
H. Zeng, A class of initial value problems for $2\times 2$ hyperbolic systems with relaxation,, J. Differential Equations, 251 (2011), 1254.
doi: 10.1016/j.jde.2011.05.018. |
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