Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains

Abstract

We consider the first mixed problem in a cylindrical domain for a pseudo-differential parabolic equation with homogeneous Dirichlet boundary conditions and a finitely supported initial function. We find upper bounds for the -norm of a solution as in terms of a geometric characteristic introduced earlier by the author for an unbounded domain , , in the case of a higher-order parabolic equation.