Carleman estimates for the wave equation in heterogeneous media with non-convex interface

A wave equation whose main coefficient is discontinuous models the evolution of waves amplitude in a media composed of at least two different materials, in which the propagation speed is different. In our mathematical setting, the spatial domain where the partial differential equation evolves is an open bounded subset of R-2 and the wave speed is assumed to be constant in each one of two sub-domains, separated by a smooth and possibly non-convex interface. This article is concerned with the construction of Carleman weights for this wave operator, allowing generalizations of previous results to the case of an interface that is not necessarily the boundary of a convex set. Indeed, using the orthogonal projection onto this interface, we define convex functions satisfying the transmission conditions imposed by the equation, such that, under usual hypothesis on the sign of the jump of the wave speed, can be used as Carleman weights. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This article focuses on a wave equation with a discontinuous main coefficient, which models the evolution of wave amplitude in a medium composed of at least two different materials with different propagation speeds. The article discusses the construction of Carleman weights for this wave operator, allowing for generalizations to interfaces that are not necessarily boundaries of convex sets.