The fundamental solution and blow-up problem of an anisotropic parabolic equation

IF 1 4区数学 Q1 MATHEMATICS

Boundary Value Problems Pub Date : 2023-09-15 DOI:10.1186/s13661-023-01780-9

Huashui Zhan

引用次数: 0

Abstract

Abstract This paper is devoted to the study of anisotropic parabolic equation related to the $p_{i}$ p i -Laplacian with a source term $f(u)$ f ( u ) . If $f(u)=0$ f ( u ) = 0 , then the fundamental solution of the equation is constructed. If there are some restrictions on the growth order of u in the source term, the initial energy $E(0)$ E ( 0 ) is positive and has a super boundedness, which depends on the Sobolev imbedding index, then the local solution may blow up in finite time.

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一类各向异性抛物方程的基本解和爆破问题

摘要本文研究了源项为$f(u)$ f(u)的与$p_{i}$ pi -拉普拉斯方程有关的各向异性抛物方程。如果$f(u)=0，则构造方程的基本解。如果源项中u的生长阶数存在一定的限制，初始能量$E(0)$ E(0)为正且具有超有界性，且该超有界性依赖于Sobolev嵌入指标，则局部解可能在有限时间内爆炸。

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

Boundary Value Problems 数学-数学

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.