Abstract
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.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 265–272 https://doi.org/10.4213/mzm13616.
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Romanov, A.V. Finite-Dimensional Reduction of Systems of Nonlinear Diffusion Equations. Math Notes 113, 267–273 (2023). https://doi.org/10.1134/S0001434623010297
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DOI: https://doi.org/10.1134/S0001434623010297