Local existence of stratified solutions to systems of balance laws (Q2756118)

The authors introduce a special class of weak solutions to a system of balance laws \(u_t+F(u)_x= f(t,x,u)\) in one space dimension. The system is required to possess a linearly degenerate eigenvalue \(\lambda\) and to admit a special symmetrizer. The introduced solutions are stratified in the sense that \(u\in L^2\cap L^\infty\) and \((\delta_t +\lambda(u) \delta_x)u\in L^2\). The assumption about the symmetrizer is used to prove energy estimates and deduce the local (in time) existence of such solutions. In particular, the solution can have an infinite local variation. For such solutions some results are proved about the propagation, the life span and the initial value problem. Examples from gas dynamics are presented (even for thermal non-equilibrium case).