Analysis on a coupled parabolic system with free boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Lu, Haihua¹  Chen, Yujuan¹  Yu, Jingqiu¹ 

[1] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

关键词: Free boundary;    Blow up;    Global fast solution;    Global slow solution;    Trichotomy;   

DOI  :  10.1016/j.jmaa.2018.08.018

来源: Elsevier

【 摘 要 】

The purpose of this paper is to investigate a parabolic problem with coupled reaction terms and free boundary, including the existence, uniqueness, regularity and long-time behavior of positive solutions. Firstly, by the contraction mapping theorem, we establish the (local) existence and uniqueness of positive solutions. Then, we prove the solution blows up in finite time with large initial data by comparison principle, and give more details for these large initial data by exhibiting an energy condition. The simultaneous blow-up result of the maximum of u and v is obtained, and the blow-up set of blow-up solutions is a compact subset of [0, h(0)]. Furthermore, there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small, while there is a global and slow solution provided that the initial datum is suitably large. Finally, for initial data sigma(phi(x), psi(x)), we obtain a trichotomy conclusion by considering the size of parameter sigma. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free