Displaying similar documents to “Travelling Waves in Near-Degenerate Bistable Competition Models”

On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion

J.A. Sherratt (2010)

Mathematical Modelling of Natural Phenomena

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Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of ...

Travelling Waves of Fast Cryo-chemical Transformations in Solids (Non-Arrhenius Chemistry of the Cold Universe)

V. Barelko, N. Bessonov, G. Kichigina, D. Kiryukhin, A. Pumir, V. Volpert (2008)

Mathematical Modelling of Natural Phenomena

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Propagation of chemical waves at very low temperatures, observed experimentally [V.V. Barelko , Advances in Chem. Phys. 74 (1988), 339-384.] at velocities of order  10 cm/s, is due to a very non- standard physical mechanism. The energy liberated by the chemical reaction induces destruction of the material, thereby facilitating the reaction, a process very different from standard combustion. In this work we present recent experimental results and develop a new mathematical model which...

Travelling Waves in Partially Degenerate Reaction-Diffusion Systems

B. Kazmierczak, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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We study the existence and some properties of travelling waves in partially degenerate reaction-diffusion systems. Such systems may for example describe intracellular calcium dynamics in the presence of immobile buffers. In order to prove the wave existence, we first consider the non degenerate case and then pass to the limit as some of the diffusion coefficient converge to zero. The passage to the limit is based on a priori estimates of solutions independent of the values of the diffusion...