Dirichlet problem for parabolic systems with Dini continuous coefficients

摘要

We consider the first initial boundary value problem for spatially one-dimensional parabolic second-order systems with Dini continuous coefficients in a semibounded domain with nonsmooth lateral boundary. We only require that the right-hand side of the boundary condition has continuous derivative of order 1/2 vanishing at t = 0. By the boundary integral equations method we construct a classical solution of this problem. The smoothness of the solution is studied.