离散方程、离散变换和离散边界值问题

Pub Date : 2024-02-26 DOI:10.1134/s0012266123120108

E. B. Afanas’eva, V. B. Vasil’ev, A. B. Kamanda Bongay

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引用次数: 0

摘要

摘要我们研究了平面扇形中离散椭圆伪微分方程的可解性。利用符号的特殊因子化，问题被简化为两变量解析函数的边界值问题。得到了一种积分变换的周期性类似方法，该方法被用于构造圆锥域中椭圆伪微分方程的解。用这种变换描述了所考虑的离散方程的一般解公式和一些边界值问题。

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Discrete Equations, Discrete Transformations, and Discrete Boundary Value Problems

Abstract

We study the solvability of discrete elliptic pseudodifferential equations in a sector of the plane. Using special factorization of the symbol, the problem is reduced to a boundary value problem for analytic functions of two variables. A periodic analog of one integral transformation is obtained that was used to construct solutions of elliptic pseudodifferential equations in conical domains. The formula for the general solution of the discrete equation under consideration and some boundary value problems are described in terms of this transformation.

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