Homogenized equation of second-order accuracy for conductivity of laminates
Kaplunov J. Panasenko G. Prikazchikova L.
2022Taylor and Francis Ltd.
Applicable Analysis
2022#101Issue 113886 - 3894 pp.
The high order homogenization techniques potentially generate the so-called infinite order homogenized equations. Since long ago, the coefficients at higher order derivatives in these equations have been calculated within various refined theories for both periodic composites and thin structures. However, it was not always clear, what is a well-posed mathematical formulation for such equations. In the present paper, we discuss two techniques for constructing a second-order homogenized equation. One of them is concerned with the projection of a weak formulation of the original problem on an ‘ansatz subspace’. The second one corresponds to the traditional two scale asymptotic expansion using the representation of a second-order corrector via the solution of the classical (leading order) homogenized equation.
35B27 , 78M35 , high order homogenized equation , Homogenization
Text of the article Перейти на текст статьи
Keele University, Keele, United Kingdom
Faculty of Mechanics and Mathematics, al-Farabi Kazakh National University, Almaty, Kazakhstan
ICJ, University Jean Monnet, Saint-Etienne, France
Institute of Applied Mathematics, Vilnius University, Vilnius, Lithuania
Moscow Power Engineering Institute, Moscow, Russian Federation
Keele University
Faculty of Mechanics and Mathematics
ICJ
Institute of Applied Mathematics
Moscow Power Engineering Institute
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026