Uniqueness of solutions to initial-boundary value problems for parabolic systems with Dini-continuous coefficients in a semibounded domain on the plane
Abstract:
The first and second initial-boundary value problems for second-order parabolic systems with coefficients satisfying the Dini condition in a semibounded plane domain with a nonsmooth lateral boundary admitting cusps are considered. Theorems on the uniqueness of classical solutions of these problems in the class of functions that are continuous and bounded together with their first spatial derivatives in the closure of this domain are proved.
Key words:parabolic systems, initial-boundary value problems, uniqueness of a classical solution, nonsmooth lateral boundary, boundary integral equations.
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