Strongly anisotropic diffusion problems; asymptotic analysis

Mihai Bostan (1)

1 I2M - Institut de Mathématiques de Marseille

The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrices have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them and establish convergence results. The analysis relies on averaging techniques, which have been used previously for studying transport equations whose advection fields have disparate components.

Mots clés: Anisotropic diffusion; Variational methods; Multiple scales; Average operator AMS classification: 35Q75; 78A35

Domaines: Equations aux dérivées partielles [math.AP]

Mihai Bostan. Strongly anisotropic diffusion problems; asymptotic analysis. Electronic Journal of Differential Equations, 2014, 256, pp.1043-1092. ⟨10.1016/j.jde.2013.10.008⟩. ⟨hal-01266552⟩