Global fast and slow solutions of a localized problem with free boundary

查看全文 作　　者：ZHOU [1]Peng;LIN [2]ZhiGui

机构地区：[1]Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;[2]School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

出　　处：《Science China Mathematics》索引2012年第55卷第9期,共14页

基　　金：supported by National Natural Science Foundation of China (Grant Nos.11071209 and 10801115);the PhD Programs Foundation of Ministry of Education of China (Grant No.20113250110005) 摘　　要：In this paper,we consider a localized problem with free boundary for the heat equation in higher space dimensions and heterogeneous environment.For simplicity,we assume that the environment and solution are radially symmetric.First,by using the contraction mapping theorem,we prove that the local solution exists and is unique.Then,some sufficient conditions are given under which the solution will blow up in finite time.Our results indicate that the blowup occurs if the initial data are sufficiently large.Finally,the long time behavior of the global solution is discussed.It is shown that the global fast solution does exist if the initial data are sufficiently small,while the global slow solution is possible if the initial data are suitably large. 关键词：自由边界问题异构环境时间行为热传导方程空间尺寸径向对称映射定理本地化

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Global fast and slow solutions of a localized problem with free boundary

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