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Homogenization of a semilinear heat equation. (English. French summary) Zbl 1372.35024
The authors study the homogenization of a semilinear heat equation with vanishing diffusivity and with an oscillating positive right-hand side (some sort of potential, chemical reaction, etc.). According to the rate between the frequency of oscillations in the production term (r.h.s.) and the vanishing factor in front of the diffusivity, the authors obtain different regimes in the limit evolution and discuss the locally uniform convergence of the solutions to the effective problem. The interesting feature of the mathematical model is that in the strong diffusion regime the effective operator is discontinuous in the gradient entry.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
35D40 Viscosity solutions to PDEs
35K58 Semilinear parabolic equations
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