Large time behaviors of solutions to the unipolar hydrodynamic model of semiconductors with physical boundary effect

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hui Sun, Ming Mei, Kaijun ZhangAbstractIn this paper, we study the asymptotic behaviors in time of solutions to the unipolar hydrodynamic model of semiconductors in the form of Euler–Poisson equations on the half line with the boundary effect, where the boundary conditions are proposed physically as the inflow/outflow/impermeable boundary or the insulating boundary. Different from the Cauchy problem, the boundary effect causes some essential difficulties in determining the asymptotic profiles for the solutions and occurs the boundary layers. First of all, by heuristically analyzing, we reasonably propose some additional boundary conditions at far field to the corresponding steady-state equations such that the steady-state systems are well-posed. Thus, we can determine the corresponding steady-states as the expected asymptotic profiles for the solutions of original IBVPs. Secondly, there are some L2-boundary-layers between the solutions of original IBVPs and their steady-states. After investigating the exact form of gaps, we technically construct some correction functions to delete these gaps. Finally, by using the energy estimates, we further prove that the original solutions of the inflow/outflow/impermeable problem (insulating problem) time-exponentially (time-exponentially/algebraically) converge to their asymptotic profiles. Finally, we carry out some numerical simulation...

Source: Nonlinear Analysis: Real World Applications - November 29, 2019 Category: Research Source Type: research