Blow-up of Solutions for a Problem with Balakrishnan-Taylor Damping and Nonlocal Singular Viscoelastic Equations-Reference-Cited by-同舟云学术

Blow-up of Solutions for a Problem with Balakrishnan-Taylor Damping and Nonlocal Singular Viscoelastic Equations

Published:2024-01-19 Issue: Volume: Page:293-315
ISSN:2581-8147
Container-title:Earthline Journal of Mathematical Sciences
language:en
Short-container-title:EJMS

Author:

Alaeddine Draifia¹

Affiliation:

1. Institute of Sciences, Department of Mathematics and Informatics, University Center Aflou, Laghouat, Algeria

Abstract

In this paper, we study the nonlinear one-dimensional viscoelastic nonlocal problem with Balakrishnan-Taylor damping terms and nonlinear source of polynomial type. We demonstrate that the nonlinear source of polynomial type is able to force solutions to blow up infinite time even in presence of stronger damping with non positive initial energy combined with a positive initial energy.

Publisher

Earthline Publishers

Reference31 articles.

1. Cahlon, D., & Shi, P. (1995). Stepwise stability for the heat equation with a nonlocal constraint. SIAM Journal on Numerical Analysis, 32, 571-593. https://doi.org/10.1137/0732025

2. Mesloub, S., & Lekrine, N. (2004). On a nonlocal hyperbolic mixed problem. Acta Scientiarum Mathematicarum (Szeged), 70, 65-75.

3. Ewing, R., & Lin, T. (1991). A class of parameter estimation techniques for fluid flow in porous media. Advances in Water Resources, 14, 89-97. https://doi.org/10.1016/0309-1708(91)90055-S

4. Shi, P. (1993). Weak solution to an evolution problem with a non-local constraint. SIAM Journal on Mathematical Analysis, 24(1), 46-58. https://doi.org/10.1137/0524004

5. Choi, Y., & Chan, K. (1992). A parabolic equation with nonlocal boundary conditions arising from electrochemistry. Nonlinear Analysis, 18, 317-331. https://doi.org/10.1016/0362-546X(92)90148-8