Homogenization of a semilinear heat equation

Annalisa Cesaroni (Padova, Italy)

I will discuss the homogenization of a semilinear heat equation with vanishing viscosity and oscillating  potential depending on u/eps.  According to the rate between frequency of oscillations and vanishing factor in the viscosity, we obtain different limit behaviour of the solutions.  In the weak diffusion regime, the effective operator is discontinuous in the gradient entry, an unusual phenomenon in homogenization, and makes the analysis of the limit more challenging. Joint work with Dirr (Cardiff) and Novaga (Pisa).

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