Results 1 to 10 of about 50 (50)
Advances in Nonlinear Analysis, 2022 In this article, we establish a viscosity method for random homogenization of an obstacle problem with nondivergence structure. We study the asymptotic behavior of the viscosity solution uε{u}_{\varepsilon } of fully nonlinear equations in a perforated ...
Lee Ki-Ahm, Lee Se-Chan
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Advanced Nonlinear Studies, 2023 In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating (N+1)\left(N+1)-dimensional thin domains (i.e., a family of bounded open sets from RN+1{{\mathbb{R}}}^{N+1}, with corrugated bounder ...
Nakasato Jean Carlos +1 more
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Journal of Function Spaces, Volume 9, Issue 1, Page 17-40, 2011., 2011 We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as ε → 0 of the solutions uε of the nonlinear equation divaε(x, ∇uε) = divbε, where both aε and bε oscillate rapidly on several microscopic scales and aε satisfies certain continuity, monotonicity and
Andreas Almqvist +4 more
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Mathematical analysis and homogenization of the torsion problem
Journal of Function Spaces, Volume 6, Issue 2, Page 155-176, 2008., 2008 In this paper we address the limitations of the classical formulation of the torsion problem and give a self‐contained survey of the function spaces and formulations that are more suitable for analysing the torsional behavior of composite materials. We also prove some homogenization results for the torsion problem in both the periodic and stochastic ...
Dag Lukkassen +3 more
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Localization and multiplicity in the homogenization of nonlinear problems
Advances in Nonlinear Analysis, 2019 We propose a method for the localization of solutions for a class of nonlinear problems arising in the homogenization theory. The method combines concepts and results from the linear theory of PDEs, linear periodic homogenization theory, and nonlinear ...
Bunoiu Renata, Precup Radu
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Bounds on the effective behavior of a homogenized generalized Reynolds equation
Journal of Function Spaces, Volume 5, Issue 2, Page 133-150, 2007., 2007 We study upper and lower bounds for estimating the effective behavior described by homogenizing a problem which is a generalization of the Reynold equation. All cases when these bounds coincide are also found.
Dag Lukkassen +3 more
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Compactness by Coarse-Graining in Long-Range Lattice Systems
Advanced Nonlinear Studies, 2020 We consider energies on a periodic set ℒ{\mathcal{L}} of the form ∑i,j∈ℒaijε|ui-uj|{\sum_{i,j\in\mathcal{L}}a^{\varepsilon}_{ij}\lvert u_{i}-u_{j}\rvert}, defined on spin functions ui∈{0,1}{u_{i}\in\{0,1\}}, and we suppose that the typical range of the
Braides Andrea, Solci Margherita
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Two‐scale convergence with respect to measures and homogenization of monotone operators
Journal of Function Spaces, Volume 3, Issue 2, Page 125-161, 2005., 2005 In 1989 Nguetseng introduced two‐scale convergence, which now is a frequently used tool in homogenization of partial differential operators. In this paper we discuss the notion of two‐scale convergence with respect to measures. We make an exposition of the basic facts of this theory and develope it in various ways.
Dag Lukkassen +2 more
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Homogenization in elastodynamics with force term depending on time
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 10, Page 723-728, 2000., 2000 We extend the study on the homogenization problem for an elastic material containing a distributed array of gas bubbles to the case when the body force depends on time. By technically constructing an approximating sequence, we are able to show the convergence of semigroups and therefore prove the main result that such spongy material can be ...
Ping Wang
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Advances in Nonlinear Analysis, 2018 One of the main goals of this paper is to extend some of the mathematical techniques of some previous papers by the authors showing that some very useful phenomenological properties which can be observed at the nano-scale can be simulated and justified ...
Díaz Jesús Ildefonso +3 more
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