Displaying similar documents to “Dynamics of Propagation Phenomena in Biological Pattern Formation”

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...

Atherosclerosis Initiation Modeled as an Inflammatory Process

N. El Khatib, S. Génieys, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL...