Well-posedness of the hydrodynamic model for semiconductors

Abstract

This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasi-linear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L(2) sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L(2) sense. The well-posedness of the model under the boundary conditions is demonstrated.