Propagation acceleration in reaction diffusion equations with anomalous diffusions

Nonlinear Evolution Equations with Anomalous Diffusions

French and Polish teams have a record of successful collaborations which resulted in methods and results that are actually attracting a growing interest of the applied mathematics community. In this new project, the participants aim at understanding the role of anomalous diffusions in two important classes of nonlinear evolution equations: kinetic equations with a Lévy-Fokker-Planck operator an...

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...

Front propagation in hyperbolic fractional reaction-diffusion equations.

From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition...

Reaction-Diffusion equations with applications

Nepomnyashchy reaction systems − Fronts in anomalous diffusion

Supplementary data rsta.2012.0179.DC1.html http://rsta.royalsocietypublishing.org/content/suppl/2012/11/23/ "Presentation at Turbulent Mixing and Beyond conference" References 79.full.html#ref-list-1 http://rsta.royalsocietypublishing.org/content/371/1982/201201 This article cites 62 articles Subject collections (52 articles) mathematical physics • collections Articles on similar topics can be...