Exploring Well-Posedness and Asymptotic Behavior in an Advection-Diffusion-Reaction (ADR) Model
<|reference_start|>Exploring Well-Posedness and Asymptotic Behavior in an Advection-Diffusion-Reaction (ADR) Model: 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.<|reference_end|>
@article{elghandouri2024exploring,
    title={Exploring Well-Posedness and Asymptotic Behavior in an
  Advection-Diffusion-Reaction (ADR) Model},
    author={Mohammed Elghandouri, Khalil Ezzinbi and Lamiae Saidi},
    journal={arXiv preprint arXiv:2403.02339},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.02339},
    primaryClass={math.AP cs.NA math.DS math.NA}
}