Hopf Bifurcation and Exchange of Stability in Diffusive Media

@article{Brand2004HopfBA,
title={Hopf Bifurcation and Exchange of Stability in Diffusive Media},
author={Thomas Brand and Markus Kunze and Guido Schneider and Thorsten Seelbach},
journal={Archive for Rational Mechanics and Analysis},
year={2004},
volume={171},
pages={263-296}
}
• Published 1 February 2004
• Mathematics
• Archive for Rational Mechanics and Analysis
Abstract.We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses a continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a pair of imaginary eigenvalues crosses the imaginary axis. For a reaction-diffusion-convection system we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a Hopf…
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Keywords: spectral gaps ; existence ; bifurcation ; unbounded ; selfadjoint operator ; real Hilbert space ; bounded ; selfadjoint operators ; bound states ; nonlinear ; Schrodinger equations ;