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

Anna Kostianko; Sergey Zelik

doi:10.3934/cpaa.2017116

Article Contents

2017, Volume 16, Issue 6: 2357-2376. Doi: 10.3934/cpaa.2017116

This issue Previous Article Dynamics of a Class of ODEs via Wavelets Next Article

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

Anna Kostianko and
Sergey Zelik^,

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

* Corresponding author
* Corresponding author

Received: February 28, 2017

Revised: March 31, 2017

Published: September 2017

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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Abstract

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.

Keywords:

Inertial manifolds,
convective reaction-diffusion equation.

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

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