Solvability of the Boundary Value Problem for a System of Parabolic Equations

ABSTRACT In this article, a boundary value problem for a parabolic equation with convection is considered. To solve the problem, a fundamental solution of a parabolic equation with almost periodic coefficients is constructed using the Levy parametrix method. An additional problem is investigating to establish a sufficient condition for the existence and uniqueness of an almost periodic solution to a boundary value problem by means of a special choice of the initial function. Sufficient conditions are obtained for the solvability of a boundary value problem with a half‐space boundary condition for a parabolic equation with variable coefficients.