Solvability of the linear inverse problem for the pseudoparabolic equation

We investigate the solvability of inverse problems of determination, along with the solution $u(x, t)$ to the pseudoparabolic equation, of the unknown source function. Similar problems are considered when studying wave processes, filtration in porous media, and heat transfer processes. A theorem for the existence of a regular solution is proved. Inverse problems for pseudoparabolic equations with an unknown external influence depending on $x$ and a final redefinition have not been considered previously.