Global existence and nonexistence of solutions for quasilinear parabolic equation
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
Boundary Value Problems 2014, 2014:33 doi:10.1186/1687-2770-2014-33Published: 7 February 2014
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.