SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Global existence and nonexistence of solutions for quasilinear parabolic equation

Xianghui Xu1, Yong-Hoon Lee1 and Zhong Bo Fang2*

Author Affiliations

1 Department of Mathematics, Pusan National University, Busan, 609-735, Republic of Korea

2 School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China

For all author emails, please log on.

Boundary Value Problems 2014, 2014:33  doi:10.1186/1687-2770-2014-33

Published: 7 February 2014

Abstract

This work is concerned with the global existence and nonexistence of solutions for a quasilinear parabolic equation with null Dirichlet boundary condition. Based on the Galerkin approximation technique and the theory of a family of potential wells, we obtain the invariant sets and vacuum isolating of global solutions including critical case, and we also give global nonexistence.

MSC: 35A01, 35B06, 35B08.

Keywords:
family of potential wells; global existence; nonexistence; vacuum isolating; critical value