Hyperbolic to parabolic relaxation theory for quasilinear first order systems
This paper is concerned with a quasilinear first-order system with a source term, and investigates the relaxation phenomena where the relaxed equilibria are described by means of an equation (or a system) of parabolic type. In particular a one-dimensional \(2\times 2\) system of genuinely nonlinear hyperbolic balance laws with a strong dissipative nonlinear term is analysed, and a different approach is used to study the limiting profiles in case of isentropic gas dynamics. The limiting profiles are given by the solutions of the convective linear parabolic equations, which include porous media type equation, and the convergence results are obtained. The paper may be of interest to someone working on conservation laws.
scientific article; zbMATH DE number 1454738
scientific article