Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold

Alexander V. Romanov

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arXiv · 1306.4249

Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold

Alexander V. Romanov

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Abstract

We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have asymptotically finite-dimensional dynamics in the corresponding state space. This example is more natural in the class of evolutionary equations of parabolic type than those known earlier.

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Alexander V. Romanov. 2013-06-18. Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold. https://arxiv.org/abs/1306.4249

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