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Working paper

Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold

arxiv.org. math. Cornell University, 2013. No. 1306.4249.
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.