AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Electronic Research Archive Article
PDF (522.6 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Existence and nonexistence of global solutions for logarithmic hyperbolic equation

Yaojun Ye( ), Qianqian Zhu
Department of Mathematics and Statistics, Zhejiang University of Science and Technology, Hangzhou 310023, China
Show Author Information

Abstract

This article is concerned with the initial-boundary value problem for a equation of quasi-hyperbolic type with logarithmic nonlinearity. By applying the Galerkin method and logarithmic Sobolev inequality, we prove the existence of global weak solutions for this problem. In addition, by means of the concavity analysis, we discuss the nonexistence of global solutions in the unstable set and give the lifespan estimation of solutions.

Keywords

logarithmic hyperbolic equationstable and unstable setsexistence and nonexistenceglobal solutionsinitial-boundary value problem

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 30 Issue 3,
March 2022
Pages 1035-1051
DOI: 10.3934/era.2022054

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Ye Y, Zhu Q. Existence and nonexistence of global solutions for logarithmic hyperbolic equation. Electronic Research Archive, 2022, 30(3): 1035-1051. https://doi.org/10.3934/era.2022054

3

Views

0

Downloads

0

Crossref

7

Web of Science

6

Scopus
Received: 18 January 2022
Revised: 15 February 2022
Accepted: 20 February 2022
Published: 15 March 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)