Homogenization of a semilinear heat equation

Cesaroni, Annalisa, Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367 and Novaga, Matteo 2017. Homogenization of a semilinear heat equation. Journal de l'École polytechnique — Mathématiques 4 , pp. 633-660.

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Abstract

We consider the homogenization of a semilinear heat equation with vanishing viscosity and with oscillating positive potential depending on $u/\varepsilon$. According to the rate between the frequency of oscillations in the potential and the vanishing factor in the viscosity, we obtain different regimes in the limit evolution and we discuss the locally uniform convergence of the solutions to the effective problem. The interesting feature of the model is that in the strong diffusion regime the effective operator is discontinuous in the gradient entry. We get a complete characterization of the limit solution in dimension $n=1$, whereas in dimension $n>1$ we discuss the main properties of the solutions to the effective problem selected at the limit and we prove uniqueness for some classes of initial data.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Date of First Compliant Deposit:	7 June 2017
Date of Acceptance:	24 May 2017
Last Modified:	08 Nov 2023 01:39
URI:	https://orca.cardiff.ac.uk/id/eprint/101266

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