On the solvability of a nonlocal problem for a hyperbolic equation with multiple involutions

D.N. Altynbek, Batirkhan Turmetov

2026

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DOI 10.3934/dcdss.2026250
Data confidence 70 medium
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Abstract

This paper investigates a multidimensional initial-boundary value problem for a nonlocal analogue of a hyperbolic equation with spatial nonlocal operators and nonlocal boundary conditions generated by a group of involutions. The method is based on representing the solution space as a direct sum of invariant subspaces, which makes it possible to reduce the original problem to a system of classical Dirichlet, Neumann, and Robin problems. The existence and uniqueness of a classical solution are proved, and the solution is constructed in the form of a Fourier series.