Discontinuous Galerkin method for partial differential equations with blow-up solutions

报告摘要:

We will study the behavior of non-negative solutions for some time-dependent partial differential equations (PDEs). We are especially interested in solving PDEs whose exact solutions become unbounded in finite time. This phenomenon is called blow-up. In our recent work (Numer Math,124 (2013), 753-781), we have applied discontinuous Galerkin (DG) methods to obtain good approximations for hyperbolic PDEs with delta-singularity, one special unbounded singularity. We will continue this approach and solve other types of PDEs with delta-singularities and other types of blow-up solutions. Numerical experiments will be given to demonstrate the advantages for the DG methods in approximating blow-up solutions

Yang Yang简介：

密歇根理工大学助理教授。2009年获中国科学技术大学数学系学士学位。2013年获美国Brown University应用数学博士学位。同年加入密歇根理工大学数学系并担任助理教授。

Yang Yang教授的主要研究方向为应用discontinuous Galerkin ( DG) 方法求解带有发散精确解的偏微分方程。该种方程在生物，天体物理，燃烧，网络中有及其广泛的应用。其他科研领域还包括DG方法的超收敛估计及其应用，计算天理物理和等离子体等。文章多发表在SIAM J. Numer. Anal., Numer. Math., J. Comput. Phy等SCI杂志上。