Asymptotic Analysis - Volume 105, issue 1-2

Authors: Temam, Roger

Article Type: Editorial

DOI: 10.3233/ASY-171450

Citation: Asymptotic Analysis, vol. 105, no. 1-2, pp. 1-1, 2017

Authors: Reichelt, Sina

Article Type: Research Article

Abstract: Based on previous homogenization results for imperfect transmission problems in two-component domains with periodic microstructure, we derive quantitative estimates for the difference between the microscopic and macroscopic solution. This difference is of order ε ρ , where ε > 0 describes the periodicity of the microstructure and ρ ∈ ( 0 , 1 2 ] depends on the transmission condition at the interface between the two components. The corrector estimates are proved without assuming additional regularity for the local correctors using the periodic unfolding method.

Keywords: Homogenization, corrector results, error estimates, periodic unfolding, two-component domain, periodic interface, imperfect transmission

DOI: 10.3233/ASY-171432

Citation: Asymptotic Analysis, vol. 105, no. 1-2, pp. 3-26, 2017

Authors: Demengel, Françoise

Article Type: Research Article

Abstract: This paper is devoted to some Lipschitz estimates between sub- and super-solutions of Fully Nonlinear equations on the model of the anisotropic p → -Laplacian. In particular we derive from the results enclosed that the continuous viscosity solutions for the equation ∑ 1 N ∂ i ( ∂ i u | p i − 2 ∂ i u ) = f are Lipschitz continuous when sup i p i …< inf i p i + 1 , where p → = ∑ i p i e i . Show more

Keywords: Degenerate fully Nonlinear equations, p→ anisotropic Laplacian, viscosity solutions, regularity

DOI: 10.3233/ASY-171433

Citation: Asymptotic Analysis, vol. 105, no. 1-2, pp. 27-43, 2017

Authors: Ciuperca, Ionel Sorin | Palade, Liviu Iulian

Article Type: Research Article

Abstract: This paper establishes an asymptotic expansion for a second order differential equation with a small diffusion coefficient, which generalizes the configurational probability diffusion equation of the Rigid Dumbbell Model (RDM) of diluted polymer solutions theory for fast shear flows. This is a singular perturbation problem with turning point.

Keywords: Turning point asymptotic problem, rigid dumbbell polymer chain model, fast shear flows, configurational probability diffusion equation

DOI: 10.3233/ASY-171435

Citation: Asymptotic Analysis, vol. 105, no. 1-2, pp. 45-76, 2017

Authors: Baňas, Ľubomír | Mahato, Hari Shankar

Article Type: Research Article

Abstract: We consider homogenization of a phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects. The pore-scale model consists of a strongly coupled system of time-dependent Stokes–Cahn–Hilliard equations. In the considered model the fluids are separated by an evolving diffuse interface of a finite width, which is assumed to be independent of the scale parameter ϵ . We obtain upscaled equations for the considered model by a rigorous two-scale convergence approach.

Keywords: Stokes–Cahn–Hilliard equations, phase-field models, multiphase porous media flow, periodic homogenization, two-scale convergence

DOI: 10.3233/ASY-171436

Citation: Asymptotic Analysis, vol. 105, no. 1-2, pp. 77-95, 2017