On Solvability of solutions of the second initial-boundary problem for PSEUDOPARABOLIC equations WITH A SMALL PARAMETER
In the study of inverse problems of mathematical physics, an important role is played by the knowledge of the solutions of the corresponding direct (in this case, the second initial-boundary) problem. In this paper, we consider the second initial-boundary value problem for a pseudoparabolic equation with a small parameter. The theorems of existence and uniqueness of the classical solution of the second initial-boundary value problem are proved. To prove the existence and uniqueness of the solution of the problem posed, the original problem is first converted to an equivalent problem, where the initial and boundary data will be zero. Then applied the Fourier method. In the space of continuously differentiable functions, a solution is obtained, justified, and presented in the form of a series. The convergence of the solution of the initial-boundary problem for a perturbed pseudoparabolic equation to the solution of the corresponding problem for the heat equation, when a small parameter tends to zero, is shown.