Homogenization of 'viscous' Hamilton-Jacobi equations in stationary ergodic media

Lions PL; Souganidis PE

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Homogenization of 'viscous' Hamilton-Jacobi equations in stationary ergodic media

机译：平稳遍历介质中“粘性” Hamilton-Jacobi方程的均质化

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We study the homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media. The "viscosity" and the spatial oscillations are assumed to be of the same order. We identify the asymptotic (effective) equation, which is a first-order deterministic Hamilton-Jacobi equation. We also provide examples that show that the associated macroscopic problem does not admit suitable solutions (correctors). Finally, we present as applications results about large deviations of diffusion processes and front propagation (asymptotics of reaction-diffusion equations) in random environments.

机译：我们研究在平稳遍历介质中“粘性”汉密尔顿-雅各比方程的均质化。假定“粘度”和空间振荡为相同数量级。我们确定了渐近（有效）方程，它是一阶确定性的Hamilton-Jacobi方程。我们还提供了一些示例，说明相关的宏观问题不容许采用适当的解决方案（校正器）。最后，作为应用，我们给出了随机环境中扩散过程和前沿传播（反应扩散方程的渐近性）的大偏差的结果。

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《Communications in Partial Differential Equations》 |2005年第3期|共41页
作者
Lions PL; Souganidis PE;
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正文语种 eng
中图分类偏微分方程;
关键词
homogenization; random media; stationary ergodic media; stochastic homogenization; viscous Hamilton-Jacobi equations; PARTIAL-DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; STOCHASTIC HOMOGENIZATION; PDE;

机译：均质化;随机介质;平稳遍历介质;随机均质化;粘性Hamilton-Jacobi方程;局部微分方程;粘度解;随机均质化;PDE;

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专利

1. Homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media [J] . Lions PL, Souganidis PE Communications in Partial Differential Equations . 2005,第1a3期

机译：平稳遍历介质中“粘性” Hamilton-Jacobi方程的均质化
2. Correctors for the Homogenization of Hamilton-Jacobi Equations in the Stationary Ergodic Setting [J] . Pierre-Louis Lions, Panagiotis E. Souganidis Communications on Pure and Applied Mathematics . 2003,第10期

机译：平稳遍历环境中Hamilton-Jacobi方程均质化的校正子
3. 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
4. Stationary Hamilton-Jacobi Equations for Convex Control Problems: Uniqueness and Duality of Solutions [C] . Rafal Goebel Louisiana Conference on Mathematical Control Theory . 2003

机译：固定式汉密尔顿 - Jacobi等式，用于凸起控制问题：解决方案的独特性和二元性
5. 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。
6. An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems [O] . Duncan Joyce, William J. Parnell, Raphaël C. Assier, -1

机译：单向纤维增强介质均质化的积分方程法；反平面弹性和其他潜在问题
7. On the Stochastic Homogenization of Fully Nonlinear Uniformly Parabolic Equations in Stationary Ergodic Spatio-Temporal Media [O] . Lin, Jessica 2013

机译：关于完全非线性一致抛物型方程的随机均匀化平稳遍历时空媒体中的方程

Homogenization of 'viscous' Hamilton-Jacobi equations in stationary ergodic media

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