The shortest lengths and the enclosure method for time dependent problems

In this paper, we discuss the role of the shortest distance in time-dependent enclosure method for the inverse problems when the inclusions are embedded in a non-layered or two-layered medium. Furthermore, the regularity assumptions for the boundaries of the inclusions are relaxed.Comment: 21cpage

Asymptotic behavior of the indicator function in the inverse problem of the wave equation for media with multiple types of cavities

In this paper, the inverse problem of the wave equation by the enclosure method for a medium with multiple types of cavities is discussed. In the case considered here, the sign of the indicator function of the enclosure method is not determined and sign cancellation may occur, resulting in loss of information. By examining the top terms of the indicator function in detail, we show that the shortest distance to the cavities can be obtained even in such a case

The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function at a given direction of unknown discontinuity embedded in a heat conductive body from the temperature for a suitable heat flux on the lateral boundary for a fixed observation time is given.Comment: 12pages. This is the final versio