Analysis of Solutions to a Free Boundary Problem with a Nonlinear Gradient Absorption

Abstract

In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption and the free boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions on the global existence, blow-up in finite time of solutions, and blow-up sets when blow-up phenomenon occurs. Furthermore, the global solution is bounded and uniformly tends to zero, and it is either a global fast solution or a global slow solution. Finally, we obtain a trichotomy conclusion by considering the size of parameter σ.