Finite-dimensional reduction of systems of nonlinear diffusion equations

A. V. Romanov

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arXiv · 2210.00499

Finite-dimensional reduction of systems of nonlinear diffusion equations

A. V. Romanov

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Abstract

We present a class of one-dimensional systems of nonlinear parabolic equations for which long-time phase dynamics can be described by an ODE with a Lipschitz vector field in R^n. In the considered case of the Dirichlet boundary value problem sufficient conditions for a finite-dimensional reduction turn out to be much wider than the known conditions of this kind for a periodic situation.

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A. V. Romanov. 2022-10-02. Finite-dimensional reduction of systems of nonlinear diffusion equations. https://arxiv.org/abs/2210.00499

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