Global existence for hyperbolic-parabolic systems with large periodic initial data

Abstract

One considers hyperbolic--parabolic systems $ u_t+(f(u))_x=(B(u)u_x)_x$ in one space dimension. For large periodic initial data and for a wide class of such systems, we establish the global existence of ``weak'' solutions. These results can be applied to general systems provided they admit a compact invariant domain. We develop the case of a particular $2\times 2$ system, the Keyfitz--Kranzer system.