Geodesic
Equivalence of two definitions of a~generalized $L_p$ solution to the initial-boundary value problem for the wave equation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 163-168

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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 $\mu(t)$ such that the integral $\int_0^T(T-t)|\mu(t)|^p\,dt$ exists. Here we prove that this solution is a unique solution to the problem in $L_p$ that satisfies the corresponding integral identity. 
@article{TM_2014_284_a9,
     author = {V. A. Il'in and A. A. Kuleshov},
     title = {Equivalence of two definitions of a~generalized $L_p$ solution to the initial-boundary value problem for the wave equation},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {163--168},
     publisher = {mathdoc},
     volume = {284},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_284_a9/}
}
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V. A. Il'in; A. A. Kuleshov. Equivalence of two definitions of a~generalized $L_p$ solution to the initial-boundary value problem for the wave equation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 163-168. http://geodesic.mathdoc.fr/item/TM_2014_284_a9/