On the solvability of a forward nonlocal problem for a nonhomogeneous Boussinesq-type equation
In this paper, we study a direct nonlocal problem for a nonhomogeneous Boussinesq-
type equation in a bounded multidimensional domain. The problem is considered under homoge-
neous boundary conditions and a weighted integral condition involving the time variable. Using
the Fourier method and spectral expansion, we derive an explicit form of the solution. Sufficient
conditions for the existence and uniqueness of the solution are obtained, and the convergence of the
corresponding series is established.
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