Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\)

Volume 22, Issue 2, pp 110--118 http://dx.doi.org/10.22436/jmcs.022.02.02

Publication Date: July 15, 2020 Submission Date: April 22, 2019 Revision Date: February 06, 2020 Accteptance Date: February 12, 2020

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Authors

Mourad Benzahi - Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria. Abdelrahmane Zarai - Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria. Salem Abdelmalek - Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria. Samir Bendoukha - Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Saudi Arabia.

Abstract

This study establishes a novel nonexistence result for a strongly coupled viscoelastic system with Balakrishnan-Taylor damping and a nonlinear source in the whole space. Sufficient conditions ensuring the nonexistence of solutions are established using the test function method.

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Keywords

• Balakrishnan-Taylor system
• non-solvability
• memory term

MSC

•  34H10
•  34D06

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