Exploring Well-Posedness and Asymptotic Behavior in an Advection-Diffusion-Reaction (ADR) Model
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.
- N. M. Buckman. The linear convection-diffusion equation in two dimensions.
- J. Hale. Asymptotic behavior of dissipative systems (providence, ri: American mathematical society) go to reference in article (1988).
- A. Pazy. Semigroups of linear operators and applications to partial differential equations. Vol. 44. Springer Science & Business Media, 2012.
- A. D. Polyanin, V. E. Nazaikinskii. Handbook of Linear Partial Differential Equations for Engineers and Scientist. CRC Press Taylor & Francis Group LLC; 2016.
- M. F. Wheeler, et C. N. Dawson. An operator-splitting method for advection-diffusion-reaction problems. 1987.
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