Fujita type critical exponent for a free boundary problem with spatial-temporal source | |
Wang, Jie1; Cao, Jia-Feng | |
刊名 | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS |
2020-02 | |
卷号 | 51 |
关键词 | Nonlinear reaction-diffusion equation Free boundary Sharp threshold trichotomy Critical exponent |
ISSN号 | 1468-1218 |
DOI | 10.1016/j.nonrwa.2019.103004 |
英文摘要 | In this paper, we investigate a nonlinear free boundary problem incorporating with nontrivial spatial and exponential temporal weighted source. To portray the asymptotic behavior of the solution, we first derive some sufficient conditions for finite time blowup. Furthermore, the global vanishing solution is also obtained for a class of small initial data. Finally, a sharp threshold trichotomy result is provided in terms of the size of the initial data to distinguish the blowup solution, the global vanishing solution, and the global transition solution. In particular, our results show that such a problem always possesses a Fujita type critical exponent whenever the spatial source is just equivalent to a trivial constant, or is an extreme one, such as "very negative" one in the sense of measure or integral. (C) 2019 Elsevier Ltd. All rights reserved. |
资助项目 | National Natural Science Foundation of China[11701243] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
WOS记录号 | WOS:000488994500022 |
状态 | 已发表 |
内容类型 | 期刊论文 |
源URL | [http://119.78.100.223/handle/2XXMBERH/31468] |
专题 | 材料科学与工程学院 理学院 |
通讯作者 | Wang, Jie |
作者单位 | 1.Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China 2.State Key Lab Adv Proc & Recycling Nonferrous Met, Lanzhou 730050, Gansu, Peoples R China |
推荐引用方式 GB/T 7714 | Wang, Jie,Cao, Jia-Feng. Fujita type critical exponent for a free boundary problem with spatial-temporal source[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2020,51. |
APA | Wang, Jie,&Cao, Jia-Feng.(2020).Fujita type critical exponent for a free boundary problem with spatial-temporal source.NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,51. |
MLA | Wang, Jie,et al."Fujita type critical exponent for a free boundary problem with spatial-temporal source".NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 51(2020). |
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