Dirichlet problem for parabolic systems with Dini continuous coefficients on the plane

Abstract

The Dirichlet problem for a one-dimensional (with respect to x) second-order parabolic system with Dini continuous coefficients is considered in an x-semibounded domain with a nonsmooth lateral boundary from the Dini–Hölder class. The classical solvability of the problem is proved by applying the method of boundary integral equations. The only condition imposed on the right-hand side of the boundary condition is that it has a continuous derivative of order 1/2 vanishing at t = 0. The smoothness of the solution is studied.