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- Title
Homogenization limit for the diffusion equation with nonlinear flux condition on the boundary of very thin holes periodically distributed in a domain, in case of a critical size.
- Authors
Jäger, W.; Neuss-Radu, M.; Shaposhnikova, T. A.
- Abstract
The article focuses on homogenization limit in case of critical size for the diffusion equation with nonlinear flux condition on very thin holes boundary periodically distributed in a domain. It relates that effective equation comprises a sink/source term that represents macroscopic contribution of the processes on the microscopic cavities' boundary. It adds that a corrector result with respect to the energy norm is proved and the gradient of the microscopic solutions' approximation is formulated. Furthermore, the boundary terms are converted into volume terms through special test functions. Moreover, a theorem is formulated to construct a corrector and prove the improved convergence after the inequalities are satisfied.
- Subjects
BURGERS' equation; LIMIT cycles; ASYMPTOTIC homogenization; DIFFERENCE equations; CALCULUS of variations; NUMERICAL solutions to boundary value problems; FERROMAGNETIC materials; MAGNETIC domain; NONLINEAR statistical models; HOLES
- Publication
Doklady Mathematics, 2010, Vol 82, Issue 2, p736
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562410050157