Inertial manifolds for 1D reaction-diffusion-advection systems. Part II:\n periodic boundary conditions

2017/02/27 by Anna Kostianko, Kostianko, Anna, Sergey Zelik +1
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Advanced Mathematical Modeling in Engineering #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1702.08559

Abstract

This is the second part of our study of the Inertial Manifolds for 1D systems\nof reaction-diffusion-advection equations initiated in citeKZI and it is\ndevoted to the case of periodic boundary conditions. It is shown that, in\ncontrast to the case of Dirichlet or Neumann boundary conditions, considered in\nthe first part, Inertial Manifolds may not exist in the case of systems endowed\nby periodic boundary conditions. However, as also shown, inertial manifolds\nstill exist in the case of scalar reaction-diffusion-advection equations. Thus,\nthe existence or non-existence of inertial manifolds for this class of\ndissipative systems strongly depend on the choice of boundary conditions.\n

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