Shock layers interactions for a relaxation approximation to conservation laws (Q1806148)

The authors study the time-asymptotic behavior of interactions between shock waves in semilinear relaxation systems which are the approximations of scalar conservation laws in one dimension. The authors first construct the interaction of two shock profiles in the \(2\times 2\) case, then prove that there exists a unique solution and an approximate solution which can be constructed by shock profiles in \(L^1\). The authors also consider the case of a \(2N\times 2N\) system with a \(L^\infty\) bound for its solution and the case without an a priori \(L^\infty\) bound respectively.