Semi-linear Elliptic and Parabolic Equations in Unbounded Domains
主 题: Semi-linear Elliptic and Parabolic Equations in Unbounded Domains
报告人: Prof. Henri BERESTYCKI (Ecole des hautes études en sciences sociales - Paris)
时 间: 2007-06-05 下午 4：00－5：00
地 点: 中关村资源大厦12层1213房间
It is a classical result that a semi-linear elliptic equation with concave type non-linearity in a bounded domain with Dirichlet condition has a unique positive solution. This talk is concerned with extensions of this result to unbounded domains. I will present several results on this theme, reporting on joint works with Fran?ois Hamel, Lionel Roques and Luca Rossi. These involve the principal eigenvalue of a linear elliptic operator. I will describe extensions of this notion to unbounded domain and their properties. I will also discuss some applications to propagation phenomena for nonlinear parabolic equations.