题   目：On optimal shape in a thermal insulation problem

报告人：Dr. Qinfeng Li （Department of Mathematics, UTSA,德州大学圣安东尼奥，USA）

摘  要: In this talk, we will study the existence and stability of the optimal shape in a thermal insulation problem. The problem is to minimize the functional：\begin{align}J_m(u,\Omega):=\frac{1}{2}\int_{\Omega}|\nablau|^2dx+\frac{1}{2m}\left(\int_{\partial\Omega}|u|d\mathcal{H}^{n1}\right)^2-\int_{\Omega} fu dx \end{align}，overall $u \in H^1(\Omega)$ and all $\Omega$ with a fixed volume in a finite container. In the above $m$ is a constant and $f\in L^2(\Omega)$ is fixed. We will develop the existence result over the so called $M$-uniform domains over which we also prove a uniform Poincare inequality, and then we will prove the existence of minimizers over a general class of configurations. We will also show that ball is a stable shape by computing the first and second variations of the functionals over pairs $(u,\mbox{ball})$. This is a joint work with Hengrong Du and Changyou Wang at Purdue University.

时  间：2019年6月13日（周四）下午4点30分

地  点：数学系一楼108报告厅

邀请人：杨孝平 老师