Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
157
Views
2
CrossRef citations to date
0
Altmetric
Articles

Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

, &
Pages 3391-3405 | Received 11 Jul 2018, Accepted 20 Jan 2020, Published online: 04 Feb 2020
 

ABSTRACT

This paper focuses on the following degenerate parabolic equation utdiv(σ(x)|u|p2u)+f(x,u)=gin Ω×R+,u=0on Ω×R+,u(x,0)=u0(x)in Ω, where Ω is a smooth bounded domain in RN,(N2),1<p<N,u0,gL1(Ω), σ(x) is positive almost everywhere and satisfies proper degenerate conditions. The existence and uniqueness result is proved in the framework of entropy solutions. For the long-time behavior, we prove the existence of a global attractor in Lq(Ω) by using some delicate estimates on the solution, which are derived by taking advantage of both the leading operator and the zero-order nonlinear term. The aforementioned results improve some previous results in the literature in several aspects.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (NSFC) [grant number 11701002, 11971031].

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.