On the Unique Solvability of the Cauchy Problem in the Class
\( C^{1,0}(\overline D)\) for Parabolic Systems on
the Plane
摘要
Abstract
The Cauchy problem for Petrovskii second-order parabolic systems in a strip on the planeis considered. The coefficients of the system satisfy the double Dini condition. The uniquesolvability of the problem in the space of functions that are continuous and bounded together withtheir first spatial derivatives in the closure of the strip is established, and the correspondingestimates are obtained. An integral representation of the solution is given.