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arXiv · 2403.02339

Exploring Well-Posedness and Asymptotic Behavior in an Advection-Diffusion-Reaction (ADR) Model

Mohammed Elghandouri·Khalil Ezzinbi·Lamiae Saidi
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Abstract

In this paper, the existence, uniqueness, and positivity of solutions, as well as the asymptotic behavior through a finite fractal dimensional global attractor for a general Advection-Diffusion-Reaction (ADR) equation, are investigated. Our findings are innovative, as we employ semigroups and global attractors theories to achieve these results. Also, an analytical solution of a two-dimensional Advection-Diffusion Equation is presented. And finally, two Explicit Finite Difference schemes are used to simulate solutions in the two- and three-dimensional cases. The numerical simulations are conducted with predefined initial and Dirichlet boundary conditions.

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Mohammed Elghandouri, Khalil Ezzinbi, Lamiae Saidi. 2024-03-04. Exploring Well-Posedness and Asymptotic Behavior in an Advection-Diffusion-Reaction (ADR) Model. https://doi.org/10.1016/j.cam.2024.116465

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