Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898705 | Journal of Differential Equations | 2018 | 44 Pages |
Abstract
In this paper we will extend the results of a trichotomy result obtained in [23] to general monostable, bistable and combustion types of nonlinearities. We show that the long-time dynamical behavior of solutions can be expressed by unified fashion, that is, for any initial data, the unique solution exhibits exactly one of the behaviors, spreading, vanishing and transition. We also give the asymptotic profile of the solution over the whole domain when spreading happens. The approach here is quite different from that used in [23].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yuki Kaneko, Hiroshi Matsuzawa,