On p-Laplacian Reaction–Diffusion Problems with Dynamical Boundary Conditions in Perforated Media

Abstract

We study the e↵ect of the p-Laplacian operator in the modelling of the heat equation through a porous medium ⇤✏ ⇢ R N (N 2). The case of p = 2 was recently published in (Anguiano, Mediterr. J. Math. 17, 18 (2020)). Using rigorous functional analysis techniques and the properties of Sobolev spaces, we managed to solve additional (nontrivial) di culties which arise compared to the study for p = 2, and we prove a convergence theorem in appropriate functional spaces.

Homogenization of a nonlinear reaction‐diffusion problem in a perforated domain with different size obstacles

“…For homogenization problems in classical periodically perforated domain, that is, the distribution period and the size of the obstacles (or holes) depend on single small scale 𝜖, besides the references mentioned above, we can also refer to refs. [32][33][34][35][36]. For homogenization problems in a perforated domain with the period and the size of the obstacles depend on two different small scales 𝜖 and 𝜖𝛿(𝜖), the problems of Stokes steady flow and Bingham flow have been considered in refs.…”

Sharp Pressure Estimates for the Navier–Stokes System in Thin Porous Media

“…Studies related to Newtonian fluids through TPM can be found in Anguiano and Suárez-Grau [11,14], Armiti-Juber [16], Bayada and et al [17], Larsson et al [26], Suárez-Grau [31], Valizadeh and Rudman [32], Wagner et al [33] and Zhengan and Hongxing [36]. Concerning generalized Newtonian fluids see Anguiano and Suárez-Grau [7,12,15], for Bingham fluids see Anguiano and Bunoiu [8,9], for compressible and piezo-viscous flow see Pérez-Ràfols et al [27], and for micropolar fluids see Suárez-Grau [30] and for diffusion problems see Anguiano [5,6] and Bunoiu and Timofte [21].…”