Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

We prove the local-in-time well-posedness of the initial boundary value problem for a system of quasilinear equations. This system is used for finding numerical stationary solutions of the hydrodynamical model of charge transport in the silicon MESFET (metal semiconductor field effect transistor). The initial boundary value problem has the following peculiarities: the quasilinear system is not a Cauchy-Kovalevskaya-type system; the boundary is a non-smooth curve and has angular points; nonlinearity of the problem is mainly connected with squares of gradients of the unknown functions. By using a special representation for the solution of a model problem we reduce the original problem to an integro-differential system. The local-in-time existence of a weakened generalized solution of this system is then proved by the fixed-point argument.