Existence and asymptotic behavior of smooth solutions to bipolar hydrodynamic model. Issue 16 (10th December 2018) - Guo, Hongxia
ABSTRACT: We are interested in the existence and asymptotic behavior of smooth solutions to the hydrodynamic model of semiconductors with non-zero doping profile. Within the insulating boundary conditions, recently, a steady state for any doping profile with large amplitude was obtained by using the calculus of variations. In this paper, the obtained steady state is regarded as the background solution. Utilizing energy methods and entropy analysis, we prove the existence of smooth solutions to the hydrodynamic model. As a by-product, we show the smooth solution convergent to the background solution with exponential decay rate.