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Zbl 1091.35011
Bellieud, Michel
Homogenization of evolution problems for a composite medium with very small and heavy inclusions. (English)
[J] ESAIM, Control Optim. Calc. Var. 11, 266-284 (2005). ISSN 1292-8119; ISSN 1262-3377/e

Summary: We study the homogenization of parabolic or hyperbolic equations like $$\rho_\varepsilon\frac{\partial^nu_\varepsilon}{\partial t^n}-\text {div}(a_\varepsilon\nabla u_\varepsilon)=f\quad\text{in}\quad \Omega \times T+\text{ boundary conditions, }n\in\{1,2\},$$ when the coefficients $\rho_\varepsilon$, $a_\varepsilon$ (defined in $\Omega)$ take possibly high values on an $\varepsilon$-periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

MSC 2000:: *35B27 Homogenization, etc.
35K05 Heat equation
35K20 Second order parabolic equations, boundary value problems
35L05 Wave equation
49J45 Optimal control problems inv. semicontinuity and convergence
74Q10 Homogenization and oscillations in dynamical problems

Keywords: limit problem; memory effects; grain-like inclusions

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