On the classical solvability of boundary value problems for parabolic equations with incompatible initial and boundary data

Abstract

We study the first and second boundary value problems for parabolic equations in a half-space ℝn+, n ≥ 2, with incompatible initial and boundary data on the boundary x n= 0 of a domain. The existence, uniqueness and estimates of the solutions in the Hölder and weighted spaces are proved. We show that nonfulfillment of the compatibility conditions leads to appearance of the solutions, which are singular in the vicinity of a boundary of a domain as t → 0.