Journal
DOKLADY MATHEMATICS
Volume 103, Issue 3, Pages 103-107Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S1064562421030030
Keywords
attractors; homogenization; reaction-diffusion equation; nonlinear equations; weak convergence; perforated domain; rapidly oscillating terms; strange term
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Funding
- Ministry of Education and Science of the Republic of Kazakhstan [AR08855579]
- Russian Foundation for Basic Research [20-01-00469]
- Russian Science Foundation [20-11-20272]
- Russian Science Foundation [20-11-20272] Funding Source: Russian Science Foundation
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The system of reaction-diffusion equations in a perforated domain with rapidly oscillating terms was studied, showing weak convergence of trajectory attractors to a homogeneous system with a strange term in the corresponding topology.
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).
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