Reiterated homogenization of hyperbolic-parabolic equations in domains with tiny holes (original) (raw)
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Homogenization Results for Hyperbolic- Parabolic Equations *
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The asymptotic behavior of the solution of a hyperbolic-parabolic equation with nonlinear sources and suitable boundary and initial conditions, defined in a perforated medium, is analyzed. We prove that the effective behavior of the solution of such a problem is governed by a parabolic equation, defined on a nonperforated domain.
Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition
Proceedings Mathematical Sciences, 2002
In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains ∂ t b x d ε , u ε − div a(u ε , ∇u ε) = f (x, t) in ε × (0, T) , u ε = 0 o n∂ ε × (0, T) , u ε (x, 0) = u 0 (x) in ε. Here, ε = \ S ε is a periodically perforated domain and d ε is a sequence of positive numbers which goes to zero. We obtain the homogenized equation. The homogenization of the equations on a fixed domain and also the case of perforated domain with Neumann boundary condition was studied by the authors. The homogenization for a fixed domain and b(x dε , u ε) ≡ b(u ε) has been done by Jian. We also obtain certain corrector results to improve the weak convergence.
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