ON INITIAL-BOUNDARY VALUE PROBLEMS FOR PARABOLIC SYSTEMS IN A SEMI-BOUNDED PLANE DOMAIN WITH GENERAL BOUNDARY CONDITIONS

The paper considers initial boundary value problems for homogeneous parabolic systems with Dini-continuous coefficients under zero initial conditions in a semi-bounded plane domain with a non- smooth lateral boundary that admits the presence of ”beaks”on which boundary conditions of a general type with variable coefficients are specified. Using the method of boundary integral equations, a theorem is proved on the unique classical solvability of such problems in the space of functions that are continuous and bounded together with their first-order spatial derivative in the closure of the domain. A representation of the solutions obtained is given in the form of vector single layer potentials.