学术报告会：Degenerate parabolic equations with nonlinear gradient terms

报告题目：Degenerate parabolic equations with nonlinear gradient terms

报告人：张正策

(西安交通大学教授、博士生导师)

时间：2019年6月28日下午3:00-4:30

地点：龙子湖校区7201

Abstract：In this talk, we survey certain results on global existence and blowup for some semilinear and quasilinear parabolic equations with nonlinear gradient terms. As an example, we consider a parabolic equation with degenerate diffusion and nonlinear gradient absorption. By a regularization approach, we first establish the local-in-time existence of its weak solutions. Then we prove the global existence by constructing a family of bounded super-solutions which technically depend on the inradius of domains. It is mentioned that we use a gradient estimate of Bernstein-type to prove that the blowup is not gradient one, but $L^\infty$ case.

个人简介：

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其应用研究。近年来，主要对非线性抛物方程的梯度爆破和自由边值问题开展定性研究，主持国家自然科学基金面上项目2项，教育部和陕西省基金各1项，在国际学术刊物CVPDE, JDE等发表论文50余篇。多次应邀参加11th AIMS(2016), AMS Spring Section(2011)等国际学术会议并作报告。