Homogenization of a nonlinear elliptic system with a transport term in L2

Article type: Research Article

Authors: Casado-Díaz, Juan^{; *}

Affiliations: Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain. E-mail: jcasadod@us.es

Correspondence: [*] Corresponding author. E-mail: jcasadod@us.es.

Abstract: We consider the homogenization of a non-linear elliptic system of two equations related to some models in chemotaxis and flows in porous media. One of the equations contains a convection term where the transport vector is only in L2 and a right-hand side which is only in L1. This makes it necessary to deal with entropy or renormalized solutions. The existence of solutions for this system has been proved in reference (Comm. Partial Differential Equations 45(7) (2020) 690–713). Here, we prove its stability by homogenization and that the correctors corresponding to the linear diffusion terms still provide a corrector for the solutions of the non-linear system.

Keywords: Nonlinear elliptic system, convection term, homogenization, entropy solutions, H-convergence, corrector

DOI: 10.3233/ASY-211729

Journal: Asymptotic Analysis, vol. 129, no. 2, pp. 273-288, 2022