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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), 987-1014.
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), 223-342.
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), 1559-1622.
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, 20, Oxford University Press, Oxford 2000. |
[5] |
C. C. Christoforou, Hyperbolic systems of balance laws via vanishing viscosity, J. Differential Equations, 221 (2006), 470-541.
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), 507-527.
doi: 10.1142/S0219891606000884. |
[7] |
C. M. Dafermos, BV solutions for hyperbolic systems of balance laws with relaxation, J. Differential Equations, 255 (2013), 2521-2533.
doi: 10.1016/j.jde.2013.07.002. |
[8] |
C. M. Dafermos, Redistribution of damping in viscoelasticity, Comm. Partial Differential Equations, 38 (2013), 1274-1286.
doi: 10.1080/03605302.2012.755544. |
[9] |
C. M. Dafermos, Heat flow with shocks in media with memory, Indiana U. Math. J., 62 (2013), 1443-1456.
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), 201-209.
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), 4014-4034.
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), 277-292.
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), 471-491.
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), 697-715.
doi: 10.1002/cpa.3160180408. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[16] |
T.-P. Liu, Admissible solutions of hyperbolic conservation laws, Memoirs AMS, 30 (1981), iv+78 pp.
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), 163-179. |
[18] |
H. Zeng, A class of initial value problems for $2\times 2$ hyperbolic systems with relaxation, J. Differential Equations, 251 (2011), 1254-1275.
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), 987-1014.
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), 223-342.
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), 1559-1622.
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, 20, Oxford University Press, Oxford 2000. |
[5] |
C. C. Christoforou, Hyperbolic systems of balance laws via vanishing viscosity, J. Differential Equations, 221 (2006), 470-541.
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), 507-527.
doi: 10.1142/S0219891606000884. |
[7] |
C. M. Dafermos, BV solutions for hyperbolic systems of balance laws with relaxation, J. Differential Equations, 255 (2013), 2521-2533.
doi: 10.1016/j.jde.2013.07.002. |
[8] |
C. M. Dafermos, Redistribution of damping in viscoelasticity, Comm. Partial Differential Equations, 38 (2013), 1274-1286.
doi: 10.1080/03605302.2012.755544. |
[9] |
C. M. Dafermos, Heat flow with shocks in media with memory, Indiana U. Math. J., 62 (2013), 1443-1456.
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), 201-209.
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), 4014-4034.
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), 277-292.
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), 471-491.
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), 697-715.
doi: 10.1002/cpa.3160180408. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[16] |
T.-P. Liu, Admissible solutions of hyperbolic conservation laws, Memoirs AMS, 30 (1981), iv+78 pp.
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), 163-179. |
[18] |
H. Zeng, A class of initial value problems for $2\times 2$ hyperbolic systems with relaxation, J. Differential Equations, 251 (2011), 1254-1275.
doi: 10.1016/j.jde.2011.05.018. |
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