Solution of the Bitsadze–Samarskii problem for a parabolic system in a semibounded domain

详细

We consider a nonlocal initial–boundary value Bitsadze–Samarskii problem for a spatially one-dimensional parabolic second-order system in a semibounded domain with nonsmooth lateral boundary. The boundary integral equation method is used to construct a classical solution of this problem under the condition that the vector function on the right-hand side in the nonlocal boundary condition only has a continuous derivative of order 1/2 vanishing at t = 0. The smoothness of the solution is studied.