Abstract

The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and Faedo–Galerkin methods with respect to the condition on the parameters in the coupling terms together with the weight condition as regards the delay terms in the feedback and the delay speed. Furthermore, we construct some convex function properties, and we prove the uniform stability estimate.

Details

Title
Global existence and exponential decay of solutions for generalized coupled non-degenerate Kirchhoff system with a time varying delay term
Author
Mezouar Nadia 1 ; Boulaaras Salah 2 

 University of Mustapha Stambouli, Department of Commerce, College of Sciences Economics, Mascara, Algeria 
 Qassim University, Department of Mathematics, College of Sciences and Arts, Al-Rass, Kingdom of Saudi Arabia (GRID:grid.412602.3) (ISNI:0000 0000 9421 8094); University of Oran 1, Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Ahmed Benbella, Algeria (GRID:grid.440479.a) (ISNI:0000 0001 2347 0804) 
Publication year
2020
Publication date
Dec 2020
Publisher
Hindawi Limited
ISSN
16872762
e-ISSN
16872770
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2401670433
Copyright
© The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.