Global existence for systems of parabolic conservation laws in several space variables (Q1092234)

The authors study systems of the form \[ \partial u/\partial t+\sum^{n}_{i=1}(\partial /\partial x_ i)f_ i(u)=D\Delta u\quad in\quad R^ n,\quad t>0. \] With given initial data. Here u and \(f_ i\) are m-vectors and D is a constant, positive matrix. They prove a global existence theorem. In particular, the result can be applied to the problem of compressible flow in higher dimensions (u denoting the velocity).