论平面上二阶抛物系统泊松势能的平滑性

Pub Date : 2024-02-26 DOI:10.1134/s0012266123120042

E. A. Baderko, K. D. Fedorov

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引用次数: 0

摘要

摘要我们考虑了一个均质二阶抛物线系统在平面条带中的考奇问题的求解。该系统的系数满足双 Dini 条件，初始函数及其一阶导数和二阶导数是连续和有界的。利用泊松势研究了该解的平滑性，并证明了相应的估计值。

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On the Smoothness of the Poisson Potential for Second-Order Parabolic Systems on the Plane

Abstract

We consider the solution of the Cauchy problem in a strip on the plane for a homogeneous second-order parabolic system. The coefficients of the system satisfy the double Dini condition. The initial function is continuous and bounded along with its first and second derivatives. Using the Poisson potential, the nature of the smoothness of this solution is studied and the corresponding estimates are proved.

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