Acta mathematica scientia, Series B >
SINGULAR LIMITS FOR INHOMOGENEOUS EQUATIONS OF ELASTICITY
Received date: 2008-12-04
Online published: 2009-05-20
Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.
LIU Yun-Guang , Christian Klingenberg . SINGULAR LIMITS FOR INHOMOGENEOUS EQUATIONS OF ELASTICITY[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 645 -649 . DOI: 10.1016/S0252-9602(09)60061-8
[1] Chueh K N, Conley C C, Smoller J A. Positive invariant regions for systems of nonlinear diffusion equations.
Indiana Univ Math J, 1977, 26: 372–411
[2] Chen G -Q, Levermore C D, Liu T -P. Hyperbolic conservation laws with stiff relaxation terms and entropy.
Comm Pure Appl Math, 1994, 47: 787–830
[3] DiPerna R J. Convergence of approximate solutions to conservation laws. Arch Rat Mech Anal, 1983, 82:
27–70
[4] Lu Y -G. Singular Limits of Stiff Relaxation and Dominant Diffusion for Nonlinear Systems. J Diff Equs,
2002, 179(2): 687–713
[5] Lu Y -G. Hyperboilc Conservation Laws and the Compensated Compactness Method. Vol 128. New York:
Chapman and Hall, CRC Press, 2003
[6] Natalini R. Convergence to equilibrium for the relaxation approximations of conservation laws. Comm
Pure Appl Math, 1996, 49: 795–823
/
| 〈 |
|
〉 |