Homogenization of a Parabolic Equation in Perforated Domain with Neumann Boundary Condition

Proceedings Mathematical Sciences

M Rajesh¹  A K Nandakumaran² 

[1] $$;Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$

关键词: Homogenization;    perforated domain;    two-scale convergence;    correctors.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domainsegin{align*}𝜕_tbleft(frac{x}{𝜀}, u_{𝜀}ight)-mathrm{div} aleft(frac{x}{𝜀}, u_{𝜀},abla u_{𝜀}ight) & = f(x,t)quadext{in}quad 𝛺_{𝜀}×(0, T), aleft(frac{x}{𝜀},u_{𝜀},abla u_{𝜀}ight).𝜐_{𝜀} & = 0 quadext{on}quad 𝜕 S_{𝜀}×(0, T), u_{𝜀} & = 0 quadext{on}quad 𝜕𝛺×(0, T), u_{𝜀}(x,0) & = u_0(x) quadext(in)quad 𝛺_{𝜀}.end{align*}Here, $𝛺_{𝜀} = 𝛺S_{𝜀}$ is a periodically perforated domain. We obtain the homogenized equation and corrector results. The homogenization of the equations on a fixed domain was studied by the authors [15]. The homogenization for a fixed domain and $bleft(frac{x}{𝜀},u_{𝜀}ight)≡ b(u_{𝜀})$ has been done by Jian [11].

【 授权许可】

Unknown