Displaying similar documents to “Relaxation oscillations in systems with different time scales”

The logarithmic delay of KPP fronts in a periodic medium

François Hamel, James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik (2016)

Journal of the European Mathematical Society

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We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.

Periodic solutions of a three-species periodic reaction-diffusion system

Tiantian Qiao, Jiebao Sun, Boying Wu (2011)

Annales Polonici Mathematici

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We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.

Pattern Formation Induced by Time-Dependent Advection

A. V. Straube, A. Pikovsky (2010)

Mathematical Modelling of Natural Phenomena

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We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators,...

The speed of propagation for KPP type problems. I: Periodic framework

Henry Berestycki, François Hamel, Nikolai Nadirashvili (2005)

Journal of the European Mathematical Society

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This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of...