Samarskii–Ionkin Type Two-Point Boundary Value Problem for a Nonhomogeneous Pseudoparabolic Equation

This paper is devoted to studying the direct and inverse problem for a nonhomogeneous pseudoparabolic equation. The equation is studied with a two-point boundary value condition recording the first variable and Samarskii–Ionkin type boundary value conditions recording the second variable. The spectral problem is studied and eigenvalues and eigenfunctions are found. The solution is constructed in the Fourier series form. Existence and uniqueness of solution’s theorems are proved.

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