On a biharmonic coupled system with non-standard nonlinearity: Existence, blow up and numerics

Article type: Research Article

Authors: Bouhoufani, Oulia^a | Messaoudi, Salim A.^{b; *} | Alahyane, Mohamed^c

Affiliations: [a] Department of Mathematics, University Batna-2, 05000 Batna, Algeria | [b] Department of Mathematics, University of Sharjah, P. O. Box 27272 Sharjah, United Arab Emirates | [c] Department of Mathematics, MIA Laboratory, La Rochelle University, 17000 La Rochelle, France

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To illustrate our theoritical findings, we present two numerical examples.

Keywords: Biharmonic operator, Existence, Blow up, Coupled system, Variable exponent, Weak solution

DOI: 10.3233/ASY-231891

Journal: Asymptotic Analysis, vol. 138, no. 1-2, pp. 69-99, 2024