An inverse blow-up problem

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• 作者：Yutaka Kamimura^a ; ^{kamimura@kaiyodai.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Hiroyuki Usami^b ; ^{husami@gifu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34A55 ; 45G05
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 December 2016
• 年：2016
• 卷：261
• 期：11
• 页码：6368-6410
• 全文大小：821 K

文摘

This paper studies an inverse problem to determine a nonlinearity of an autonomous equation from blow-up time of solutions to the equation. Firstly we prove a global continuation result showing that a nonlinearity realizing blow-up time for large initial data can be continued in the direction of smaller data as long as the blow-up time is Lipschitz continuous. Secondly we develop a method based upon a Wiener–Hopf structure by which the existence and uniqueness of a nonlinearity realizing blow-up time for large initial data is shown. These enable us to establish a global existence and uniqueness result for the inverse problem.