Global existence, nonexistence, and decay of solutions for a wave equation of p-Laplacian type with weak and p-Laplacian damping, nonlinear boundary delay and source terms

Article type: Research Article

Authors: Boumaza, Nouri^{a; c; *} | Gheraibia, Billel^{b; c}

Affiliations: [a] Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa, Algeria. E-mail: [email protected] | [b] Department of Mathematics and Computer Science, Larbi Ben M’Hidi University, Oum El-Bouaghi, Algeria. E-mail: [email protected] | [c] Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University, Tebessa, Algeria

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

Abstract: In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p>2 and p=2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.

Keywords: p-Laplacian equation, strong damping, delay term, nonlinear boundary conditions, global existence, general decay, finite time blow up

DOI: 10.3233/ASY-211742

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 577-592, 2022