The method of potentials for the heat equation with involution

This work is devoted to the study of the solvability of initial-boundary value problems for parabolic equations with involution using the potential theory method. A nonlocal parabolic equation is introduced using involutive transformations over a spatial variable. The Cauchy problem was solved, a fundamental solution was constructed, using which the heat potentials of the simple and double layers were introduced, and their properties were studied. Further, using these properties, as also applying the methods of the theory of integral equations, the first boundary value problem for a parabolic equation with involution was solved. The solution of this problem is constructed in explicit form, and the uniqueness of the solution is proven using the method of apriori estimates.

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