On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations
Pub Date : 2024-07-08
DOI:10.1134/s0012266124030054
引用次数: 0
Abstract
In a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann boundary value problems for a functional-differential equation generalizing the Euler–Poisson–Darboux equation. A sufficient condition for the solvability of the Cauchy problem is proved, and an explicit form of the resolving operator is indicated, which is written using the Bessel and Struve operator functions introduced by the author. For boundary value problems in the hyperbolic case, we establish conditions imposed on the operator coefficient of the equation and the boundary elements that are sufficient for the unique solvability of these problems.
论抽象函数微分欧拉-泊松-达布方程的初值和边界问题的可解性
摘要 在巴拿赫空间中，我们考虑了泛化欧拉-泊松-达尔布方程的函数微分方程的考希问题和狄利克特与诺伊曼边界值问题。证明了 Cauchy 问题可解性的充分条件，并指出了解析算子的明确形式，该形式是用作者引入的贝塞尔和斯特鲁夫算子函数写成的。对于双曲情况下的边界值问题，我们建立了施加于方程的算子系数和边界元素的条件，这些条件足以保证这些问题的唯一可解性。
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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