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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
DOI10.1016/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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