Hyperbolic to parabolic relaxation theory for quasilinear first order systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:162

Article

Marcati, P ; Rubino, B

关键词: compensated compactness;    compressible Euler flow;    conservation laws;    energy estimates;    entropy inequality;    hyperbolic systems;    isentropic gas dynamics;    nonlinear heal conduction;    parabolic systems;    relaxation;    rescaling;    semilinear systems;    singular limits;    Young measures;   

DOI  :  10.1006/jdeq.1999.3676

来源: Elsevier

【 摘 要 】

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 2 x 2 systems of genuinely nonlinear hyperbolic balance laws in 1 greater than or similar to 0 with a strong. dissipative term. A different method, which combines the div-curl lemma with accretive operators, is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics. We also investigate relaxation results for some 2 greater than or similar to D cases, which include the Cattaneo model for nonlinear heat conduction and the compressible Euler flow. Moreover, convergence result is also obtained for general semilinear systems in 1 greater than or similar to D. (C) 2000 Academic Press.

【 授权许可】

Free