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Article

Параболическое уравнение с нелокальной диффузией без гладкого инерциального многообразия

Математические заметки. 2014. Т. 96. № 4. С. 578-587.

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