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| HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS |
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Citation： |
P. DONATO,A. NABIL.HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS[J].Chinese Annals of Mathematics B,2004,25(2):143~156 |
| Page view： 1399
Net amount： 817 |
Authors： |
P. DONATO; A. NABIL |
Foundation： |
Project supported by the European Research and Training Network “HMS 2000” of the European Union
under Contract HPRN-2000-00109. |
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| Abstract： |
This paper is devoted to the homogenization of a semilinear
parabolic equation with rapidly oscillating coefficients
in a domain periodically perforated by $\var$-periodic holes of size $\var$. A
Neumann condition is prescribed on the boundary of the holes.
The presence of the holes does not allow to prove a compactness
of the solutions in $L^2$. To overcome this difficulty, the
authors introduce a suitable auxiliary linear problem to which a
corrector result is applied. Then, the asymptotic behaviour of
the semilinear problem as $\var\to 0$ is described, and the limit
equation is given. |
Keywords： |
Periodic homogenization, Perforated domains, Semilinear parabolic
equations |
Classification： |
35B27, 35K55 |
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