Existence of global solutions to a model of chondrogenesis

Kaźmierczak, Bogdan

doi:10.1002/mma.1034

Math Methods in App Sciences

2008

DOI: 10.1002/mma.1034

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Existence of global solutions to a model of chondrogenesis

Bogdan Kaźmierczak

Abstract: SUMMARYThe paper considers conditions sufficient for the existence of classical Csolutions to a new model of chondrogenesis during the vertebrate limb formation. We assume that the diffusion coefficient of the fibronectin is positive and that the function describing the interaction between the fibronectin and cells satisfies some additional properties.

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2011

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Reaction–diffusion model of atherosclerosis development

et al. 2011

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Atherosclerosis begins as an inflammation in blood vessel walls (intima).The inflammatory response of the organism leads to the recruitment of monocytes. Trapped in the intima, they differentiate into macrophages and foam cells leading to the production of inflammatory cytokines and further recruitment of white blood cells. This self-accelerating process, strongly influenced by low-density lipoproteins (cholesterol), results in a dramatic increase of the width of blood vessel walls, formation of an atherosclerotic plaque and, possibly, of its rupture. We suggest a 2D mathematical model of the initiation and development of atherosclerosis which takes into account the concentration of blood cells inside the intima and of pro-and antiinflammatory cytokines. The model represents a reaction-diffusion system in a strip with nonlinear boundary conditions which describe the recruitment of monocytes as a function of the concentration of inflammatory cytokines. We prove the existence of travelling waves described by this system and confirm our previous results which suggest that atherosclerosis develops as a reaction-diffusion wave. The theoretical results are confirmed by the results of numerical simulations.

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Reaction–diffusion model of atherosclerosis development

et al. 2011

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Existence of global solutions to a model of chondrogenesis

Cited by 1 publication

References 21 publications

Reaction–diffusion model of atherosclerosis development

Reaction–diffusion model of atherosclerosis development

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