Approximation of the inertial manifold for a nonlocal dynamical system

Xingjie Yan; Jinchun He; Jinqiao Duan

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arXiv · 1403.0165

Approximation of the inertial manifold for a nonlocal dynamical system

Xingjie Yan·Jinchun He·Jinqiao Duan

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Abstract

We consider inertial manifolds and their approximation for a class of partial differential equations with a nonlocal Laplacian operator $-(-\Delta)^{\frac{\alpha}{2}}$, with $0<\alpha<2$. The nonlocal or fractional Laplacian operator represents an anomalous diffusion effect. We first establish the existence of an inertial manifold and highlight the influence of the parameter $\alpha$. Then we approximate the inertial manifold when a small normal diffusion $\varepsilon \Delta$ (with $\varepsilon \in (0, 1)$) enters the system, and obtain the estimate for the Hausdorff semi-distance between the inertial manifolds with and without normal diffusion.

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Xingjie Yan, Jinchun He, Jinqiao Duan. 2014-03-02. Approximation of the inertial manifold for a nonlocal dynamical system. https://arxiv.org/abs/1403.0165

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