Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
170
Views
3
CrossRef citations to date
0
Altmetric
Articles

Blow-up phenomena for p-Laplacian parabolic equations under nonlocal boundary conditions

&
Pages 3350-3365 | Received 18 Sep 2019, Accepted 12 Jan 2020, Published online: 23 Jan 2020
 

Abstract

The purpose of this paper is to deal with the blow-up problems of the following p-Laplacian parabolic equations with nonlocal boundary conditions: h(u)t=|u|p2u+k1(t)f(u)in Ω×(0,t),|u|p2uν=k2(t)Ωg(u)dxon Ω×(0,t),u(x,0)=u0(x)0in Ω¯, where p>2, ΩRn (n2) is a bounded convex region, and the boundary Ω is smooth. With the help of differential inequality techniques and Sobolev inequalities, we prove that the blow-up does occur on some certain conditions of the data. In addition, we obtain upper bounds and lower bounds of the blow-up time in ΩRn (n2).

AMS CLASSIFICATIONS:

Acknowledgments

The authors are greatly indebted to the reviewers for many helpful suggestions and comments.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 61473180).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.