Global existence, nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations

Abstract

In this paper, we study the Cauchy problem of semilinear heat equations. By introducing a family of potential wells, we first prove the invariance of some sets and isolating solutions. Then we obtain a threshold result for the global existence and nonexistence of solutions. Finally we discuss the asymptotic behavior of the solution. © 2007 Elsevier Ltd. All rights reserved.