Homogenization of forward‐backward parabolic equations

Article type: Research Article

Authors: Amar, M.^; | Dall'Aglio, A. | Paronetto, F.

Affiliations: Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, Via A. Scarpa 16, 00161 Roma, Italy E‐mails: {amar, aglio}@dmmm.uniroma1.it | Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, Via per Arnesano, 73100 Lecce, Italy E‐mail: fabio.paronetto@unile.it

Note: [] Corresponding author.

Abstract: We study the homogenization of the equation \[R(\varepsilon ^{-1}x)\frac{ \curpartial u_{\varepsilon }}{\curpartial t}-\Delta u_{\varepsilon }=f,\] where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.

Journal: Asymptotic Analysis, vol. 42, no. 1-2, pp. 123-132, 2005