ON THE UNIQUE SOLVABILITY OF THE CAUCHY PROBLEM IN THE CLASS

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Abstract

The Cauchy problem for Petrovskii second-order parabolic systems in a strip on the plane is considered. The coefficients of the system satisfy the double Dini condition. The unique solvability of the problem in the space of functions that are continuous and bounded together with their spatial derivatives of the first order in the closure of the strip is established and corresponding estimates are obtained. An integral representation of the solution is given.

About the authors

E. A Baderko

Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Email: baderko.ea@yandex.ru

S. I Sakharov

Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Email: ser341516@yandex.ru

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