Diffusion approximation for nonlinear evolutionary equations with large interaction and fast boundary fluctuation |
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Authors: | Yan Lv Wei Wang |
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Affiliation: | 1. School of Science, Nanjing University of Science and Technology, Nanjing, China;2. Department of Mathematics, Nanjing University, Nanjing, China |
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Abstract: | 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. |
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Keywords: | 34C15 37H10 60H10 Diffusion approximations Martingale Fast boundary oscillation Neumann operator |
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