Geodesic
On attractors of reaction–diffusion equations in a porous orthotropic medium
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 10-15

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A system of reaction–diffusion equations in a perforated domain with rapidly oscillating terms in the equation and in the boundary conditions is studied. A nonlinear function in the equations may not satisfy the Lipschitz condition and, hence, the uniqueness theorem for the corresponding initial–boundary value problem for the considered system of reaction–diffusion equations may not be satisfied. It is proved that the trajectory attractors of this system weakly converge in the corresponding topology to the trajectory attractors of the homogenized reaction–diffusion system with a “strange term” (potential).
Keywords: attractors, homogenization, reaction–diffusion equation, nonlinear equations, weak convergence, perforated domain, rapidly oscillating terms strange term. 
@article{DANMA_2021_498_a1,
     author = {K. A. Bekmaganbetov and V. V. Chepyzhov and G. A. Chechkin},
     title = {On attractors of reaction{\textendash}diffusion equations in a porous orthotropic medium},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {10--15},
     publisher = {mathdoc},
     volume = {498},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a1/}
}
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K. A. Bekmaganbetov; V. V. Chepyzhov; G. A. Chechkin. On attractors of reaction–diffusion equations in a porous orthotropic medium. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 10-15. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a1/