勷勤数学•专家报告

题      目：The Cauchy problem for a parabolic p-Laplacian equation with combined nonlinearities

报  告  人：张正策 教授  (邀请人：潘洪京)

                                      西安交通大学

时      间： 11月30日  14：30-15:30

地     点：数科院西楼111报告厅

报告人简介:

       张正策, 西安交通大学数学与统计学院教授、博士生导师，主要从事非线性偏微分方程理论及应用研究，重点开展非线性抛物方程梯度爆破和自由边值问题的定性分析。在Sci. China Math., CVPDE, JDE, JDDE, JNS, SIAM  J. Numer. Anal.等学术期刊发表九十余篇论文, 主持多项国家自然科学基金面上项目和省部级基金, 多次应邀参加AIMS和AMS Spring Section等国际学术会议并作报告。

摘      要：

         In this talk, we consider the critical exponents for the homogeneous evolution p-Laplacian equation 

$u_{t}-\Delta_{p}u=u^{m}+|\nabla u|^{q}$ and its inhomogeneous version 

$u_{t}-\Delta_{p}u=u^{m}+|\nabla u|^{q}+h(x)$ in $\mathbb{R}^{N}\times\mathbb{R}^{+}$, 

$u\geq0$, $u(x,0)=u_{0}(x)$ in $\mathbb{R}^{N}$, 

where $N\geq1$, $p, m>1$ and $q>1$. We obtain a discontinuous critical exponent result for the homogeneous evolution p-Laplacian equation, which demonstrates the gradient term brings about a significant phenomenon of the critical exponent, changing from $m=p-1+p/N$ to $m=\infty$ as $q$ goes to the value $p-N/(N+1)$ from above. Meanwhile, we also investigate the inhomogeneous evolution p-Laplacian equation and get a different discontinuous critical exponent result. This is a joint work with Heqian Lu.

        欢迎老师、同学们参加、交流！