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Uniqueness of Solutions to Initial Boundary Value Problems for Parabolic Systems in Plane Bounded Domains with Nonsmooth Lateral Boundaries
Doklady Mathematics ( IF 0.6 ) Pub Date : 2021-01-14 , DOI: 10.1134/s1064562420050269 E. A. Baderko , M. F. Cherepova
中文翻译:
具有非光滑横向边界的平面有界域上抛物型系统初边值问题解的唯一性
更新日期:2021-01-14
Doklady Mathematics ( IF 0.6 ) Pub Date : 2021-01-14 , DOI: 10.1134/s1064562420050269 E. A. Baderko , M. F. Cherepova
Abstract
We consider initial boundary value problems with boundary conditions of the first or second kind for one-dimensional (with respect to a spatial variable) Petrovskii parabolic systems of the second order with variable coefficients in a bounded domain with nonsmooth lateral boundaries. The uniqueness of regular solutions to these problems in the class of functions that are continuous in the closure of the domain together with their first spatial derivatives is established using the boundary integral equation method.
中文翻译:
具有非光滑横向边界的平面有界域上抛物型系统初边值问题解的唯一性
摘要
我们考虑一阶(相对于空间变量)一维(相对于空间变量)第二类Petrovskii抛物型系统的边界条件存在初始边界值问题,该系统具有可变系数,且边界域具有非平滑的横向边界。使用边界积分方程法建立了在闭合域中连续的函数类别中这些问题的常规解及其唯一的空间导数的唯一性。