Development for inverse boundary value problems using asymptotic analysis of resolvents

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400170
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Hiroshima University
• Principal Investigator: Kawashita Mishio 広島大学, 理学(系)研究科(研究院), 教授 (80214633)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: レゾルベント / 境界値逆問題 / 囲い込み法 / 漸近展開 / ポテンシャル論

Outline of Final Research Achievements

In the boundary value inverse problem of a heat equation, the information on cavities or inclusions are deduced from the analysis of the asymptotic behavior of the function called an "indicator function." The aim of this research is to obtain this information via analysis of the asymptotic behavior of the resolvents. First, a domain including this cave is given only from one observational data by showing detailed estimation of an integral kernel for a strictly convex cave. This result is extended to the case of several strictly convex cavities. This problem setup is natural extension of the inverse problem for one-dimensional case. Furthermore, through this research, it became clear that there is a close relation to the asymptotic behavior of indicator functions and resolvents.

Free Research Field

偏微分方程式論