Spectral analysis of localized rotating waves in parabolic systems.

ABSTRACT: In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (λ1,…,λ d )=(±iσ1,…,±iσk ,0,…,0). The spectra of these linearized operators are crucial for the nonlinear stability of rotating waves in reaction-diffusion systems. We prove under appropriate conditions that every [Formula: see text] satisfying the dispersion relation [Formula: see text]belongs to the essential spectrum [Fo

SUBMITTER: Beyn WJ 

PROVIDER: S-EPMC5869616 | biostudies-literature | 2018 Apr

REPOSITORIES: biostudies-literature