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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 22
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 5, October 2015
  4. Homogenization of diffusion problems with a nonlinear interfacial resistance
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 6, December 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 5, October 2015
Large time behavior of solutions for a complex-valued quadratic heat equation
The role of the mean curvature in a Hardy–Sobolev trace inequality
On the spectrum of a Baouendi–Grushin type operator: an Orlicz–Sobolev space setting approach
On the viscosity solutions to Trudinger’s equation
Periodic, quasi-periodic and unbounded solutions of radially symmetric systems with repulsive singularities at resonance
Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains
Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models
Existence of heteroclinic solution for a class of non-autonomous second-order equation
Global existence and uniqueness for the inhomogeneous 1-Laplace evolution equation
Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition
Exponential stabilization of a viscoelastic wave equation with dynamic boundary conditions
Second order mean field games with degenerate diffusion and local coupling
A $${C^{1,\alpha}}$$ C 1 , α partial regularity result for non-autonomous convex integrals with discontinuous coefficients
Homogenization of diffusion problems with a nonlinear interfacial resistance
On invariant tori of vector field under weaker non-degeneracy condition
Nonautonomous fractional problems with exponential growth
Scalar field equation with non-local diffusion
Two solutions for a singular elliptic problem indefinite in sign
The homogeneous Hénon–Lane–Emden system
Collective periodicity in mean-field models of cooperative behavior
Nodal set of strongly competition systems with fractional Laplacian
On the Brezis–Lieb lemma without pointwise convergence
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 4, August 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 3, June 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 2, April 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 1, February 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Homogenization of diffusion problems with a nonlinear interfacial resistance

Content Provider SpringerLink
Author Le Nguyen, Kim Hang Donato, Patrizia
Copyright Year 2015
Abstract In this paper, we consider a stationary heat problem on a two-component domain with an ε-periodic imperfect interface, on which the heat flux is proportional via a nonlinear function to the jump of the solution, and depends on a real parameter γ. Homogenization and corrector results for the corresponding linear case have been proved in Donato et al. (J Math Sci 176(6):891–927, 2011), by adapting the periodic unfolding method [see (Cioranescu et al. SIAM J Math Anal 40(4):1585–1620, 2008), (Cioranescu et al. SIAM J Math Anal 44(2):718–760, 2012), (Cioranescu et al. Asymptot Anal 53(4):209–235, 2007)] to the case of a two-component domain. Here, we first prove, under natural growth assumptions on the nonlinearities, the existence and the uniqueness of a solution of the problem. Then, we study, using the periodic unfolding method, its asymptotic behavior when $${\varepsilon\to 0}$$ . In order to describe the homogenized problem, we complete some convergence results of Donato et al. (J Math Sci 176(6):891–927, 2011) concerning the unfolding operators and we investigate the limit behaviour of the unfolded Nemytskii operators associated to the nonlinear terms. According to the values of the parameter γ we have different limit problems, for the cases $${\gamma < -1, \gamma =-1}$$ and $${\gamma \in \left] -1,1\right]}$$ . The most relevant case is $${\gamma =-1}$$ , where the homogenized matrix differs from that of the linear case, and is described in a more complicated way, via a nonlinear function involving the correctors.
Ending Page 1380
Page Count 36
Starting Page 1345
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 5
Volume Number 22
Language English
Publisher Springer Basel
Publisher Date 2015-05-08
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Homogenization; equations in media with periodic structure Interface problems; diffusion-limited aggregation Nonlinear interface conditions Analysis Nonlinear boundary value problems for linear elliptic equations Periodic homogenization Elliptic equations with jump
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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