Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems
نویسنده
چکیده
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 22 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A diierent method, which combines the div-curl lemma with accretive operators, is then applied to study the limiting prooles in the case of nonhomogeneous isentropic gas dynamics. We also investigate relaxation results for some 2-D cases, which include the Cattaneo model for nonlinear heat conduction and the compressible Euler ow. Moreover, convergence result is also obtained for general semilinear systems in 1-D.
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