Asymptotic solutions that can describe the incidence and reflection of waves have been used in various situations. They can also be applied to inverse problems and provide useful information in situations where a precise evaluation is required. However, the construction of standard asymptotic solutions requires higher regularity with respect to the boundaries of the observation target. This article proposes a “modified asymptotic solution” to overcome this weakness. To demonstrate its usefulness, it is applied to the analysis of the indicator function in the enclosure method for the inverse problem of the wave equation in a mixed-type medium.
Kawashita et al. (Fri,) studied this question.