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Homogenization of semilinear parabolic equations in domains with spherical traps. (English) Zbl 0878.35013

We consider a semilinear parabolic problem in a domain with a large number of perforated spheres periodically distributed with a dimensionalized period of order \(\varepsilon\). Moreover, the perforations radii are very small (of order \(\varepsilon^{n/(n-2)})\) compared to the sphere’s radius (of order \(\varepsilon)\) making them behaving like “traps”. It is shown that the homogenization of this problem leads to a system of a nonlinear parabolic p.d.e. coupled with an o.d.e. defining then a relaxation time.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs

Keywords:

relaxation time
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References:

[1] DOI: 10.1016/0362-546X(92)90015-7 · Zbl 0779.35011 · doi:10.1016/0362-546X(92)90015-7
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