Geodesic
Finite-Dimensional Reduction of Systems of Nonlinear Diffusion Equations
Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 265-272.

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We present a class of one-dimensional systems of nonlinear parabolic equations for which the phase dynamics at large time can be described by an ODE with a Lipschitz vector field in $\mathbb R^n$. In the considered case of the Dirichlet boundary value problem, the sufficient conditions for a finite-dimensional reduction turn out to be much wider than the known conditions of this kind for a periodic situation.
Keywords: nonlinear parabolic equations, finite-dimensional dynamics on an attractor, inertial manifold. 
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A. V. Romanov. Finite-Dimensional Reduction of Systems of Nonlinear Diffusion Equations. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 265-272. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a8/

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