General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

Salah Boulaaras; Fares Kamache; Youcef Bouizem; Rafik Guefaifia

doi:10.1186/s13661-020-01470-w

Boundary Value Problems (Nov 2020)

General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

Salah Boulaaras,
Fares Kamache,
Youcef Bouizem,
Rafik Guefaifia

Affiliations

Salah Boulaaras: Department of Mathematics, College of Sciences and Arts, Qassim University
Fares Kamache: Department of Mathematics, Faculty of Exact Sciences, University Tebessa
Youcef Bouizem: Department of Mathematics, Faculty of Mathematics and Informatics, USTOMB
Rafik Guefaifia: Department of Mathematics, College of Sciences and Arts, Qassim University

DOI: https://doi.org/10.1186/s13661-020-01470-w
Journal volume & issue: Vol. 2020, no. 1
pp. 1 – 24

Abstract

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Abstract The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.

35L35
35L20

Published in Boundary Value Problems

ISSN: 1687-2762 (Print); 1687-2770 (Online)
Publisher: SpringerOpen
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics: Analysis
Website: http://www.boundaryvalueproblems.com/

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Abstract

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