Nagayasu, Sei:Post Doctorial Fellow,Analysis

Keyword(s):
Inverse problems, wave equations, elastic equations, nondestructive inspections, layered media.
Research Interest:
Partial differential equations
Research Activities:
I am interested in inverse problems of partial differential equations (PDEs), in particular reconstruction procedures in the nondestructive inspections for layered media. We can usually observe only the surface of the object, and we cannot directly observe its inside. The nondestructive inspection is one of the methods in order to guess the information of the inside. The method is as follows. We first create an artificial explosion at a certain point near the surface of the object. Then waves generated by the explosion travel in the object. We observe the waves on its surface, and guess the structure of the object from the observation data. This is the nondestructive inspection. We formulate this problem mathematically. The behaviors of the waves in the object are described by PDEs. The coefficients of PDEs mean the property of the object. The solutions of PDEs mean the behaviors of the waves. Then the nondestructive inspection is the problem that we determine the coefficients from the part of the solution. This problem is one of the inverse problems.