The Cauchy–Neumann problem for a multidimensional nonisentropic hydrodynamic semiconductor model

We investigate a multidimensional nonisentropic hydrodynamic model for semiconductors, where the energy-conserved equation with nonzero thermal conductivity coefficient is contained. We establish the global existence of smooth solutions for the Cauchy–Neumann problem with small perturbed initial data and Neumann boundary values. We prove that the solutions converge to the stationary solutions of the corresponding drift-diffusion equations; that is, the solutions tend to the stationary solution exponentially fast as t → +∞. Moreover, the existence and uniqueness of the stationary solutions to the corresponding drift-diffusion equations are obtained.