小非整数阶畸变椭圆方程的边界值问题求解

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-08 DOI:10.1134/s0012266124030066

D. P. Emel’yanov

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引用次数: 0

摘要

摘要我们考虑了矩形内不规则非整阶退化椭圆方程的 Dirichlet 边界值问题。微分算子的系数应该是解析的。我们利用奇点谱分离的方法，以数列的形式构造了一个正式的解；解在（y=0 \）附近对变量 \（y\）的非解析依赖性的特征被明确写出。我们用格林函数法证明了数列对经典解的收敛性。

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Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy

Abstract

We consider the Dirichlet boundary value problem for an elliptic type equation with irregular noninteger-order degeneration in a rectangle. The coefficients of the differential operator are supposed to be analytic. We construct a formal solution by using the method of spectral separation of singularities in the form of a series; the character of the nonanalytic dependence of the solution on the variable \(y\) in a neighborhood of \(y=0 \) is written out explicitly. We prove the convergence of the series to the classical solution using the Green’s function method.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.