Homogenization of semilinear parabolic equations in domains with spherical traps

Abstract

The semilinear parabolic problem in a domain in Rⁿ with a large number of periodically located and perforated spheres is considered. It is assumed that the period of the structure is ε and that the radius of the perforations is of order ε^n/n-2 . The homogenization of this problem leads to a system of a non linear parabolic p.d.e. coupled with a non linear o.d.e.

Keywords:

• Homogenization
• asymptotic behavior
• domains with “traps”

¹UMR-CNRS 5545, Lyon-StEtienne, 23 rue Paul Michelon, 42023 Saint-Etienne Cedex 2, France, [email protected]

²Mathematical Division, Institute for Low Temperature Physics, 47 Lenin ave., 310164, Kharkov, Ukraine, [email protected]

¹UMR-CNRS 5545, Lyon-StEtienne, 23 rue Paul Michelon, 42023 Saint-Etienne Cedex 2, France, [email protected]

²Mathematical Division, Institute for Low Temperature Physics, 47 Lenin ave., 310164, Kharkov, Ukraine, [email protected]

Notes

¹UMR-CNRS 5545, Lyon-StEtienne, 23 rue Paul Michelon, 42023 Saint-Etienne Cedex 2, France, [email protected]

²Mathematical Division, Institute for Low Temperature Physics, 47 Lenin ave., 310164, Kharkov, Ukraine, [email protected]