Open AccessFinal dynamics of systems of nonlinear parabolic equations on the circle
Author(s) -
A. V. Romanov
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021776
Subject(s) - ode , dissipative system , lipschitz continuity , mathematics , class (philosophy) , nonlinear system , parabolic partial differential equation , convection , mathematical analysis , field (mathematics) , vector field , dynamics (music) , physics , pure mathematics , geometry , partial differential equation , mechanics , computer science , thermodynamics , quantum mechanics , artificial intelligence , acoustics
We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamics of a system can be described by an ODE with Lipschitz vector field in $ \mathbb{R}^{N} $. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.