ON THE SOLVABILITY OF THE FIRST INITIAL-BOUNDARY VALUE PROBLEM FOR PARABOLIC SYSTEMS IN A BOUNDED DOMAIN WITH NON-SMOOTH LATERAL BOUNDARIES ON THE PLANE

The first initial-boundary value problem for Petrovskii second-order parabolic system in a bounded domain on the plane is investigated. The coefficients of the system satisfy the double Dini condition. The lateral boundaries of the domain admit cusps at the initial moment of time. The question of the existence of a solution to that problem in the space of functions that are continuous and bounded together with their highest derivatives in the closure of the domain is studied. An integral representation of that solution is obtained. Corresponding estimates are established.