Determination of a nonlinearity from blow-up time

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Yutaka Kamimura¹  Hiroyuki Usami² 

[1] Department of Ocean Sciences, Tokyo University of Marine Science and Technology;Faculty of Engineering, Gifu University

关键词: Inverse problem;    blow-up time;    multiplicative Wiener-Hopf.;   

DOI  :  10.3792/pjaa.90.127

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We study an inverse problem to determine a nonlinearity of an autonomous equation from a blow-up time of solutions of the equation. A local well-posedness of the inverse problem near a nonlinearity of the type $u^{1+\sigma}$, $\sigma>0$, is established. The paper also suggests that the inverse problem has a good, mathematical structure from a viewpoint of the Wiener-Hopf theory in integral equations.

【 授权许可】

Unknown