On Solvability of a Mixed Problem for a Fifth Order Linear Partial Differential Equations with Parameter

In this paper, we consider a linear fifth order partial differential equation with initial value and Dirichlet boundary value conditions. The Fourier spectral method of separation of variables is applied. The countable system of linear Volterra integral equations is obtained. Theorem on a unique solvability of countable system of integral equations is proved. The method of successive approximations is used. The unique solution of the mixed problem is obtained in the form of Fourier series. Absolutely and uniformly convergence of Fourier series is proved. Stability of the solution with respect to parameter is proved.