学术报告

【online】Sub-exponential convergence to steady-states for the Euler-Poisson equations......

发布人:发布时间: 2021-04-23

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题目:Sub-exponential convergence to steady-states for the Euler-Poisson equations with time-dependent damping  

 

报告人:张凯军 教授(东北师范大学)

 

摘要: In this talk, we study the large time behavior of smooth solutions to the unipolar isentropic hydrodynamic model of semiconductors with time-dependent damping $-\frac{n \boldsymbol u}{(1+t)^\lambda}$ for $\lambda\in(-1,1)$. Here, it is called the strong damping when $\lambda<0$ and weak damping when $\lambda>0$; while it is called the regular damping when $\lambda=0$. Firstly, we consider the one-dimensional Cauchy problem, where  $\lambda\in(-1,0)\cup(0,1)$.  For the strong damping case with $\lambda\in(-1,0)$,  the system is proved to possess a unique global smooth solution time-asymptotically converging to the stationary solution of the unipolar drift-diffusion model for semiconductors in the sub-exponential rate of $(1+t)^{|\lambda|}e^{-\alpha(1+t)^{1-|\lambda|}}$ for the constant $\alpha>0$. For the weak damping case with $\lambda\in(0,1)$,  when the doping profile is  a positive constant,  the system is further proved to admit a unique global smooth  solution converging to a constant state in the sub-exponential rate of $(1+t)^{-\frac{|\theta+\lambda|}{2}}e^{-\beta(1+t)^{1-|\lambda|}}$ for the constant $\beta>0$, where the index $\theta\in[\lambda,\infty)$ relies on the initial perturbation.  Secondly,  we study the multi-dimensional Cauchy problem, where $\lambda\in(0,1)$. When  the doping profile is a positive constant,  the system is proved to admit a unique smooth  solution which converges  to a constant state in the sub-exponential rate of $(1+t)^{-\frac{\vartheta+\lambda}{2}}e^{-\eta(1+t)^{1-\lambda}}$ for $\eta>0$, where the index $\vartheta\in[\lambda,\infty)$ still relies on the initial perturbation.  This is the first mathematical result of the Euler-Poisson equations with time-dependent damping.

 

时间:202142910:00-12:00

 

方式:腾讯会议   ID387 419 257  密码:210429

 

邀请人:栗付才 老师