On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $$\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}$$

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-06-04 DOI:10.3103/s1066369x24700105

A. Yu. Trynin

引用次数: 0

Abstract

The paper proposes a new method for obtaining a generalized solution to the mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions to the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.

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论使用算子 $$\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}} 求解抛物型方程混合边界值问题的一种方法

摘要本文提出了一种新方法，用于求解具有第三类边界条件和连续初始条件的抛物方程的混合边界值问题的广义解。广义函数是从序列方法的意义上理解的。序列类的代表是广义函数，它是利用函数插值算子得到的，而函数插值算子是利用考奇问题的解构建的。解是以在解域内均匀收敛的级数形式获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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