Diffusion approximation for nonlinear evolutionary equations with large interaction and fast boundary fluctuation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Lv, Yan¹  Wang, Wei² 

[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing, Jiangsu, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

关键词: Diffusion approximations;    Martingale;    Fast boundary oscillation;    Neumann operator;   

DOI  :  10.1016/j.jde.2018.09.001

来源: Elsevier

【 摘 要 】

Approximations are derived for both nonlinear heat equations and singularly perturbed nonlinear wave equations with highly oscillating random force on boundary and strong interaction. By a diffusion approximation method, if the interaction is large and the singular perturbation is small enough, the approximation of the nonlinear wave equation is an one dimensional stochastic ordinary differential equation with white noise from the boundary which is exactly the same as that of the nonlinear heat equation. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free