Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy
Pub Date : 2024-07-08
DOI:10.1134/s0012266124030066
引用次数: 0
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.
小非整数阶畸变椭圆方程的边界值问题求解
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。
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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