Study and suppression of singularities in wave-type evolution equations on non-convex domains with cracks

Abstract

One of the objectives of this paper is to establish the exact controllability for wave-type evolution equations on non-convex and/or cracked domains with non-concurrent support crack lines. Admittedly, we know that according to the work of Grisvard P., in domains with corners or cracks, the formulas of integrations by parts are subject to geometric conditions: the lines of cracks or their supports must be concurrent. In this paper, we have established the exact controllability for the wave equation in a domain with cracks without these additional geometric conditions.