Initial-Boundary Value Problems for Parabolic Systems in a Semibounded Plane Domain with General Boundary Conditions

Abstract

Initial-boundary value problems are considered for homogeneous parabolic systems with Dini-continuous coefficients and zero initial conditions in a semibounded plane domain with a nonsmooth lateral boundary admitting cusps, on which general boundary conditions with variable coefficients are given. A theorem on unique classical solvability of these problems in the space of functions that are continuous and bounded together with their first spatial derivatives in the closure of the domain is proved by applying the boundary integral equation method. A representation of the resulting solutions in the form of vector single-layer potentials is given.