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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: dos Santos, Bruna C. | Oliva, Sergio M. | Rossi, Julio D.
Article Type: Research Article
Abstract: In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of smaller dimension) and as a limit problem we obtain coupling between local and nonlocal equations acting in domains of different dimension. We find existence and uniqueness of solutions and we prove several qualitative properties (like conservation of mass and convergence to the mean value of the initial condition as time goes to infinity).
Keywords: Nonlocal diffusion, heat equation, asymptotic behavior
DOI: 10.3233/ASY-211740
Citation: Asymptotic Analysis, vol. 129, no. 3-4, pp. 545-575, 2022
Authors: Boumaza, Nouri | Gheraibia, Billel
Article Type: Research Article
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
Citation: Asymptotic Analysis, vol. 129, no. 3-4, pp. 577-592, 2022
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