Graph representation for asymptotic expansion in homogenisation of nonlinear first-order equations

Nenad AntonićKre?imir Burazin

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Graph representation for asymptotic expansion in homogenisation of nonlinear first-order equations

机译：非线性一阶方程均化中渐近展开的图表示

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摘要

Homogenisation of a linear transport equation leads to an integro-differential equation with the differential part of the same type as the starting equation. The (non-periodic) homogenisation of semilinear transport equations is open. In order to pinpoint technical difficulties, as a first step in that direction, following the approach of Tartar we consider an ordinary differential equation with an oscillating coefficient a

机译：线性输运方程的均质化导致一个积分微分方程，其微分部分的类型与起始方程相同。半线性输运方程的（非周期）均化是开放的。为了查明技术难题，作为该方向的第一步，按照Tartar的方法，我们考虑一个振荡系数为a的常微分方程。

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《Annali dell'Universita di Ferrara》 |2007年第2期|149-176|共28页
作者
Nenad AntonićKre?imir Burazin;
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作者单位

Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, Croatia;

Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia;

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正文语种 eng
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关键词
Homogenisation; Memory effects; Nonlinear equations;

机译：均质化;记忆效应;非线性方程;

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专利

1. On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case [J] . Nesterov A.V. Computational mathematics and mathematical physics . 2012,第7期

机译：临界情况下具有小非线性的一阶偏微分方程奇摄动系统解的渐近性
2. Asymptotic representations of solutions of essentially nonlinear systems of ordinary differential equations with regularly and rapidly varying nonlinearities [J] . Evtukhov V.M., Shlepakov O.R. Ukrainian mathematical journal . 2013,第9期

机译：具有非线性且迅速变化的常微分方程基本非线性系统解的渐近表示。
3. ASYMPTOTIC REPRESENTATIONS OF RAPIDLY VARYING SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH RAPIDLY AND REGULARLY VARYING NONLINEARITIES [J] . O. O. Chepok Journal of Mathematical Sciences . 2021,第1期

机译：快速和定期不同非线性的二阶微分方程迅速变化溶液的渐近表示
4. Asymptotic expansions of the solutions of nonlinear evolution equations [C] . Lukomsky, V.P., Bobkov, . 1996

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5. Asymptotic expansion of ODE type solutions to nonlinear diffusion equations [D] . Eom Junyong 2019

机译：非线性扩散方程的ODE型解的渐近展开。
6. Corrigendum to On a Nonlinear Wave Equation Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters [O] . Le Thi Phuong Ngoc, Le Khanh Luan, Tran Minh Thuyet, 2017

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7. Asymptotic expansion of solutions to the nonlinear Schrodinger equations (Harmonic Analysis and Nonlinear Partial Differential Equations) [O] . 和田健志 2001

机译：非线性Schrodinger方程（调和分析和非线性偏微分方程）的解的渐近展开
8. Homogenisation by Multiple Scales Expansion of the Navier Stokes Equations.Scientific Report [R] . Fureby, C. 2000

机译：Navier stokes方程的多尺度扩张均匀化。科学报告

Graph representation for asymptotic expansion in homogenisation of nonlinear first-order equations

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