# American Institute of Mathematical Sciences

November  2017, 16(6): 2357-2376. doi: 10.3934/cpaa.2017116

## Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions

 University of Surrey, Department of Mathematics, Guildford, GU2 7XH, United Kingdom

* Corresponding author

Received  March 2017 Revised  April 2017 Published  July 2017

Fund Project: 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.

This is the first part of our study of inertial manifolds for the system of 1D reaction-diffusion-advection equations which is devoted to the case of Dirichlet or Neumann boundary conditions. Although this problem does not initially possess the spectral gap property, it is shown that this property is satisfied after the proper non-local change of the dependent variable. The case of periodic boundary conditions where the situation is principally different and the inertial manifold may not exist is considered in the second part of our study.

Citation: Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
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