Show simple item record

dc.contributor.authorMezouar, Nadia ( )
dc.contributor.authorAbdelli, Mama ( )
dc.contributor.authorRachah, Amira ( Orcid Icon 0000-0002-9643-5054 )
dc.date.accessioned2022-03-31T17:07:04Z
dc.date.available2022-03-31T17:07:04Z
dc.date.issued2017-02-27
dc.identifier.citationMezouar, N., Abdelli, M., & Rachah, A. (2017). Existence of global solutions and decay estimates for a viscoelastic Petrovsky equation with a delay term in the non-linear internal feedback. Electronic Journal of Differential Equations, 2017(58), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15584
dc.description.abstract

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with a delay term in the weakly nonlinear internal feedback:

|ut|lutt + ∆2u - ∆utt - ∫0t h(t - s)∆2u(s) ds
+ μ1g1 (ut(x, t)) + μ2g2 (ut(x, t - τ)) = 0

We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.

dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectGlobal solutionen_US
dc.subjectDelay termen_US
dc.subjectGeneral decayen_US
dc.subjectMultiplier methoden_US
dc.subjectWeak frictional dampingen_US
dc.subjectConvexityen_US
dc.subjectViscoelastic Petrovsky equationen_US
dc.titleExistence of global solutions and decay estimates for a viscoelastic Petrovsky equation with a delay term in the non-linear internal feedbacken_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record