Universidad de Granada
Title
Modelling through nonlinear flux-limited spreading
Abstract
Reaction-diffusion equations are nowadays a basic tool in the modelling of populations whose dynamics is basically ruled by two processes: local reactions, in which the populations interact between themselves, and diffusion, which makes the populations spread out in the physical space.
In the ambient of embryonic morphogenesis [1], it has been proposed the adaptation of the classical linear diffusion mechanism (Fick’s Law) by considering flux-limited operators. The employment of limited diffusion ideas in biological ambients provokes new mathematical questions concerning pattern formation or even qualitative behavior. This talk is devoted to present recent advances in the analysis of traveling waves to some flux-limited reaction-diffusion models where the classical traveling wave profiles will coexist with discontinuous waves spreading through the medium with finite speed [2, 3].
References
[1] M. Verbeni, O. Sánchez, E. Mollica, I. Siegl-Cachedenier, A. Carlenton, I. Guerrero, A. Ruiz i Altaba, J. Soler, Morphogenetic action through flux-limited spreading, Physics of Life Reviews 10 (2013), 457–475.
[2] J. Campos, P. Guerrero, O. Sánchez., J. Soler, On the analysis of traveling waves to a nonlinear flux limited reaction-diffusion equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 30(1) (2013), 141–155.
[3] J. Calvo, J. Campos, V. Caselles, O. Sánchez., J. Soler, Pattern formation in a flux limited reaction-diffusion equation of porous media type, preprint.
