Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 3
150
Views
8
CrossRef citations to date
0
Altmetric
Articles

Global existence and decay for a system of two singular one-dimensional nonlinear viscoelastic equations with general source terms

, &
Pages 824-848 | Received 14 May 2019, Accepted 17 Apr 2020, Published online: 30 Apr 2020
 

ABSTRACT

The paper studies a system of two singular one-dimensional nonlinear equations that arise in generalized viscoelasticity with long-term memory, with general source terms and nonlocal boundary condition. We prove the existence of a global solution to the problem using the potential-well theory. Furthermore, we construct a Lyapunov functional and use it together with the perturbed energy method to prove a general decay result.

2000 Mathematics Subject Classifications:

Acknowledgments

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions which helped them to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

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.