Homogenization of nonlinear parabolic equations with hysteresis

Achille Landri; Pokam Kakeu; Jean Louis Woukeng

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Homogenization of nonlinear parabolic equations with hysteresis

机译：非线性抛物方程与滞后的均质化

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摘要

This work is concerned with the homogenization of initial boundary value parabolic equations with hysteresis, containing nonlinear monotone operators in the diffusion term. We make use of the sigma-convergence concept together with the properties of hysteresis operator to derive the homogenized problem. The homogenized operator is obtained in terms of a solution of a nonlinear corrector problem posed and solved in the usual sense of distributions.We also provide an approximation scheme for the homogenized coefficient.

机译：本文研究了扩散项中含有非线性单调算子的滞后抛物型初边值方程的均匀化问题。我们利用sigma收敛概念，结合滞回算子的性质，导出了均匀化问题。均匀化算子是通过一个非线性校正问题的解来获得的，该问题是在通常的分布意义下提出并求解的。我们还提供了均匀化系数的近似格式。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2020年第10期|共22页
作者
Achille Landri; Pokam Kakeu; Jean Louis Woukeng;
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作者单位

Department of Mathematics and Computer Science University of Dschang P.O. Box 67 Dschang Cameroon;

Department of Mathematics and Computer Science University of Dschang P.O. Box 67 Dschang Cameroon;

Department of Mathematics and Computer Science University of Dschang P.O. Box 67 Dschang Cameroon;

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原文格式 PDF
正文语种 eng
中图分类应用数学;力学;
关键词
corrector problem; homogenization; hysteresis; nonlinear parabolic equation;

机译：校正器问题;均质化;滞后;非线性抛物线方程;

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2. Homogenization of attractors for a class of nonlinear parabolic equations [J] . WANG Guo-lian, ZHANG Xing-you 重庆大学学报（英文版） . 2004,第002期
3. HOMOGENIZATION FOR NONLINEAR SCHR(O)DINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES [J] . Binhua FENG, Dun ZHAO, Chunyou SUN 数学物理学报（英文版） . 2015,第003期
4. A homogenization result for a parabolic equation with Preisach hysteresis [J] . J. Kopfova Zeitschrift fur Angewandte Mathematik und Mechanik . 2007,第5期

机译：具有Preisach磁滞的抛物方程的均质化结果
5. On the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media [J] . Lin Jessica Journal of Differential Equations . 2015,第3期

机译：平稳遍历时空介质中完全非线性一致抛物线方程的随机均质化
6. Erratum to: Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations [J] . Hubert Nnang Nonlinear Differential Equations and Applications NoDEA . 2012,第6期

机译：勘误到：弱阻尼非线性双曲抛物方程的确定性同质化
7. Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation [C] . Pavel S. Petrov, Andrey G. Tyshchenko, Matthias Ehrhardt International Conference on Days on Diffraction . 2018

机译：近似非线性亥姆霍兹方程的迭代抛物方程的数值解
8. On the stochastic homogenization for fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. [D] . Lin, Jessica C. 2014

机译：平稳遍历时空介质中全非线性均匀抛物方程的随机均质化。
9. Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations and an Experiment in Deblurring Nonlinearly Blurred Imagery [O] . Alfred S Carasso 2013

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10. A homogenization result for a parabolic equation with Preisach hysteresis [O] . Jana Kopfová 2007

机译：具有Preisach磁滞的抛物方程的均化结果
11. How to Homogenize a Nonlinear Diffusion Equation (e.g.) Stefan's Problem [R] . Damlamian, A. 1980

机译：如何均匀化非线性扩散方程（例如）stefan问题

Homogenization of nonlinear parabolic equations with hysteresis

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