Asymptotics of the homogenized Lagrangian for the model of slow diffusion with nonlinear degeneration
type: Item
instance of: scholarly article
title: Asymptotics of the homogenized Lagrangian for the model of slow diffusion with nonlinear degeneration
zbMATH Open document ID: 0869.35013
DOI: 10.1007/BF02509559
publication date: 1997-08-25T00:00:00Z
review text: We study the asymptotic behavior of the homogenized Lagrangian for a small concentration gradient in the following model of nonlinear degenerate diffusion. Consider the local energy \(l_0(\xi_1,\xi_2)={1\over 2}(|\xi_1|-1)^2_++ {1\over 2}|\xi_2|^2\), a vector field \(v(x)\), \(v(x)\neq 0\) almost everywhere, and define the field \(\alpha(x)= v(x)/|v(x)|\) of unit vectors. Let \(T_\alpha\) be the matrix of rotation by an angle \(\alpha\). We construct a spatially nonhomogeneous Lagrangian by setting \(L(x,\xi)= l_0(T_{\alpha(x)}\xi)\) and consider the variational problem \[ \inf_u\Biggl\{\int_D [L(x,\nabla u(x))- g(x)u(x)]dx\Biggr\}. \]
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 49L99
zbMATH DE Number: 1002983
zbMATH Keywords: homogenized Lagrangian
zbMATH Keywords: nonlinear degenerate diffusion
author: Serguei M. Kozlov
MaRDI profile type: Publication
cites work: Q3996839
full work available at URL: https://doi.org/10.1007/bf02509559
OpenAlex ID: W1995562456
Recommended article: Long-time asymptotics of non-degenerate non-linear diffusion equations
Recommended article: The asymptotic profile of solutions of degenerate diffusion equations
Recommended article: Q3199884
Recommended article: Asymptotic and other properties of a nonlinear diffusion model
Recommended article: Asymptotic properties of a reaction-diffusion equation with degenerate \(p\)-Laplacian
Recommended article: The Asymptotic Behaviour of the Solution of a Nonlinear Diffusion Equation
Recommended article: Q4291572
Recommended article: Q3333819
Recommended article: Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.
Recommended article: Simultaneous diffusion and homogenization asymptotic for the linear Boltzmann equation
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1002983