Summary: An investigation of the stability of Sobolev type equations undoubtedly is an actual problem, since these equations, with various conditions, model a multitude of processes. For example, the Barenblatt - Zheltov - Kochina model describes such processes as, for example, filtration and thermal conductivity. In this paper we consider the Cauchy - Dirichlet problem for equation in a bounded domain. We shall understand stability in the sense of Lyapunov A. M. The aim of this paper is to obtain conditions under which the stationary solution of our problem will be stable and asymptotically stable. The obtained conditions are formulated in the theorem. In addition, an algorithm of the computational experiment will be described to illustrate the instability in the case when the conditions of the theorem are not satisfied. We note that here we apply the method of the Lyapunov functional modified for the case of complete normed spaces. The computational experiment is based on the Galerkin method.