奇异抛物方程的淬火解

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-11-29 DOI:10.37394/23206.2023.22.97

A. Bouzelmate, Fatima Sennouni, A. Gmira

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引用次数: 0

摘要

本文致力于研究非线性抛物方程的自相似解。更确切地说，我们考虑以下单维方程：(E) : ut(x, t) = (u m)_xx(x, t) - |x|^q u^-p (x, t), x ∈ R, t > 0，其中 m > 1, q > 1 和 p > 0。最初，我们利用定点定理和相关的能量函数来确定解的存在性。随后，我们得出了一些关于原点附近解的渐近行为的重要结果。

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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The Quenching Solutions of a Singular Parabolic Equation

This article is dedicated to the study of the self-similar solutions of a nonlinear parabolic equation. More precisely, we consider the following uni-dimensional equation: (E) : ut(x, t) = (u m)_xx(x, t) − |x|^q u^−p (x, t), x ∈ R, t > 0, where m > 1, q > 1 and p > 0. Initially, we employed a fixed point theorem and an associated energy function to establish the existence of solutions. Subsequently, we derived some important results on the asymptotic behavior of solutions near the origin.

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.