| HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS |
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| 作者姓名： | P. DONATO A. NABIL |
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| 作者单位： | Universite de Rouen，UFR des Sciences，Laboratoire de Mathematiques Raphael Salem，site Colbert，76821 Mont Saint Aignan，France.，Universite Ibn Zohr，ENSA，BP 33/S，Agadir，Maroc. |
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| 基金项目： | Project supported by the European Research and Training Network “HMS 2000” of the European Union under Contract HPRN-2000-00109. |
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| 摘 要： | This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. 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 L2. 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 ε→ 0 is described, and the limit equation is given.
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| 关 键 词： | 均质化 周期 振荡系数 渐近性 半线性 |
| 收稿时间： | 2010/11/3 0:00:00 |
HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS |
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| P. DONATO,A. NABIL.HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS[J].Chinese Annals of Mathematics,Series B,2004,25(2):143-156. |
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| Authors: | P DONATO and A NABIL |
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| Institution: | 1. Université de Rouen, UFR des Sciences, Laboratoire de Mathématiques Raphae1 Salem, site Colbert,76821 Mont Saint Aignan, France;Université Paris VI, Laboratoire Jacques-Louis Lions, Boite courrier 187 75252 Paris Cedex, France
2. Université Ibn Zohr, ENSA, BP 33/S, Agadir, Maroc |
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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 e-periodic holes of size ε. 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 L2. 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 e → 0 is described, and the limit equation is given. |
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| Keywords: | Periodic homogenization Perforated domains Semilinear parabolic equations |
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