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The Wave Equation on Domains with Cracks Growing on a Prescribed Path: Existence, Uniqueness, and Continuous Dependence on the Data
Given a bounded open set Ω⊂Rd with Lipschitz boundary and an increasing family Γt, t∈[0,T], of closed subsets of Ω, we analyze the scalar wave equation ü−div(A∇u)=f in the time varying cracked domains Ω⧹Γt. Here we assume that the sets Γt are contained into a prescribed(d−1)-manifold of class C2. Our …