Compensated compactness for a class of hyperbolic systems of \(p\geq 3\) conservation laws
The authors consider a nonlinear coupled system of a finite number of strictly hyperbolic conservation laws where some of the equations are genuinely nonlinear whereas the others are of Temple's type, i.e. there exist invariant submanifolds of the niveau surfaces. Using the method of compensated compactness and special techniques for the analysis of Temple type systems they can show results of the following type: If \((u_\varepsilon)\) is a sequence of solutions of a parabolic regularization (vanishing viscosity method) or a Godunov scheme for the given system lying in a compact subset of \(p\)-dimensional Euclidean space (where \(p\) is the number of conservation laws) there exists a subsequence which converges weakly to an entropy solution of the system for \(\varepsilon\to 0\).
scientific article; zbMATH DE number 722307
scientific article