Final Dynamics of Systems of Nonlinear Parabolic Equations on the Circle

2020/11/03 by Romanov, A. V.
#35K57 #35K90 #35K91 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 35B41 #Secondary 35K42

paper · doi:10.48550/arxiv.2011.01822

Abstract

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 ℝ^N. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.

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