Existence and Uniqueness of Solution for a Parabolic-Hyperbolic Equation with Multiplicative Control and Nonlocal Boundary Conditions

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2024-08-17 DOI:10.1007/s11253-024-02320-z

Volodymyr Kapustyan, Ivan Pyshnograiev

引用次数: 0

Abstract

We consider a parabolic-hyperbolic equation with multiplicative control and nonlocal boundary conditions. By using the Riesz biorthogonal basis, the problem is reduced to a sequence of one-dimensional problems with alternative representations of their solutions. Conditions guaranteeing the existence and uniqueness of the solution to the analyzed problem are established.

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具有乘法控制和非局部边界条件的抛物线-超双曲方程的解的存在性和唯一性

我们考虑了一个具有乘法控制和非局部边界条件的抛物-超抛物方程。通过使用 Riesz 双正交基础，该问题被简化为一系列一维问题，其解有不同的表示方法。建立了保证所分析问题解的存在性和唯一性的条件。

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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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.