Equivalence of two definitions of a generalized L p solution to the initial-boundary value problem for the wave equation

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Abstract
In our previous papers, we introduced the notion of a generalized solution to the initial-boundary value problem for the wave equation with a boundary function µ(t) such that the integral ∫ 0 T (T − t)|µ(t)| p dt exists. Here we prove that this solution is a unique solution to the problem in L p that satisfies the corresponding integral identity.