The local Cauchy problem for dissipative plasmas

We investigate a system of partial differential equations modeling dissipative plasmas. Transport fluxes are anisotropic linear combinations of gradients and also include zeroth order contributions due to electromagnetic forces. There are also source terms depending on the solution gradient. By using entropic variables, we first recast the system in a partially symmetric form and next in the form of a quasilinear partially symmetric hyperbolic parabolic system. Using a result of Vol'Pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem.