Abstract
Abstract
The existence of a solution to the Ricquier problem with Dirichlet boundary conditions for one high-order parabolic equation in an unbounded domain is discussed. The convergence of the approximation using the Galerkin method of a generalized solution to the Ricquier problem is investigated. The dependence of behavior of the norm of the problem solution for large values of time on the geometry of an area unlimited in spatial variables lying at the base of the cylinder with a limited carrier of the initial function is considered. For a fairly wide class of unbounded domains, upper bounds for the solution of a mixed problem for a high-order parabolic equation are estimated, which are expressed in terms of simple geometric characteristics of the unbounded domain. The obtained upper estimations for the solution of the mixed problem are accurate.