Transcript Seminario di Analisi - Dipartimento di Matematica e Applicazioni

Seminario di Analisi
Dipartimento di Matematica e Applicazioni
“Renato Caccioppoli”
Università degli Studi di Napoli Federico II
Lunedı̀ 19 Dicembre 2016 – Sala Professori I Livello, h. 12:00
M ATTEO N OVAGA
H OMOGENIZATION OF SEMILINEAR HEAT EQUATIONS
A BSTRACT. I will discuss the homogenization of a semilinear heat equation with vanishing viscosity and an oscillating potential depending on the function itself.
According to the relation between frequency of the oscillations and the vanishing viscosity factor, we obtain different behaviors of the solution in the limit. In the weak diffusion
regime, the effective operator is discontinuous in the gradient entry, which is an unusual
phenomenon in homogenization and makes the analysis of the limit equation more challenging.
This is a joint work with Annalisa Cesaroni (Padova) and Nicolas Dirr (Cardiff).
D IPARTIMENTO DI M ATEMATICA - U NIVERSIT À DI P ISA
E-mail address: [email protected]