The fundamental solution and blow-up problem of an anisotropic parabolic equation-Reference-Cited by-同舟云学术

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

Published:2023-09-15 Issue:1 Volume:2023 Page:
ISSN:1687-2770
Container-title:Boundary Value Problems
language:en
Short-container-title:Bound Value Probl

Author:

Zhan Huashui

Abstract

AbstractThis 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.

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13661-023-01780-9.pdf

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