On the Well-Posedness of an Initial–Boundary Value Problem for a Degenerate Heat Equation

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010188

A. R. Zainullov, K. B. Sabitov

引用次数: 0

Abstract

The well-posedness of an initial–boundary value problem for a model parabolic equation with two power-law degeneration lines is studied. Two initial–boundary value problems depending on the degeneracy exponents are stated, and uniqueness and existence theorems are proved. The solutions of these problems are constructed in closed form.

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论退化热方程初始边界值问题的良好拟合

摘要研究了具有两条幂律退化线的模型抛物方程的初边界值问题的良好求解性。提出了两个取决于退化指数的初始边界值问题，并证明了唯一性和存在性定理。这些问题的解以封闭形式构造。

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

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.