Systems of partial differential equations of mixed hyperbolic-parabolic type (Q1881134)

The goal of this paper to formulate a general theory applicable to a broad class of physically important systems such as the Navier-Stokes equations of compressible flow, equations of compressible magnetohydrodynamics, where the authors claimed some new results, models of chemical combustion. The authors proved the global existence and uniqueness of solutions of some mixed hyperbolic-parabolic systems in one space variable with initial data which were pointwise bounded with possible large oscillations and with small total energy. When the initial energy was large, they proved the existence of local in time regular solutions.