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

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This work is partially supported by the grants 14-41-00044 and 14-21-00025 of RSF as well as grants 14-01-00346 and 15-01-03587 of RFBR.
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  • This is the second part of our study of the Inertial Manifolds for 1D systems of reaction-diffusion-advection equations initiated in [6] and it is devoted to the case of periodic boundary conditions. It is shown that, in contrast to the case of Dirichlet or Neumann boundary conditions, considered in the first part, Inertial Manifolds may not exist in the case of systems endowed with periodic boundary conditions. However, as also shown, inertial manifolds still exist in the case of scalar reaction-diffusion-advection equations. Thus, the existence or non-existence of inertial manifolds for this class of dissipative systems strongly depend on the choice of boundary conditions.

    Mathematics Subject Classification: Primary:35B40, 35B45.

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