This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

If we had to formulate in one sentence what this book is about, it might be “How partial
differential equations can help to understand heat explosion, tumor growth or evolution of …

In this paper we introduce a conceptual model for vegetation patterns that generalizes the
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …

We investigate, in a systematic fashion, coherent structures, or defects, which serve as
interfaces between wave trains with possibly different wavenumbers in reaction-diffusion …

We establish selection of critical pulled fronts in invasion processes as predicted by the
marginal stability conjecture. Our result shows convergence to a pulled front with a …

We establish nonlinear stability and asymptotic behavior of traveling periodic waves of
viscous conservation laws under localized perturbations or nonlocalized perturbations …

We present a nonlinear stability theory for periodic wave trains in reaction–diffusion systems,
which relies on pure\(L^\infty\)-estimates only. Our analysis shows that localization or …

Spiral waves are striking self-organized coherent structures that organize spatio-temporal
dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual …

We classify generic instabilities of wave trains in reaction–diffusion systems on the real line
as the wavenumber and system parameters are varied. We find three types of robust …

Pattern forming systems allow for a wealth of states, where wavelengths and orientation of
patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns …