In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified...

This paper deals with the principle of groundwater pollution. The basic equation for pollution distribution is the diffusion equation. In the natural but also economical science different kinds of this equation are used. This work focuses on the convection-diffusion equation. Using this equation the diffusive behavior of the pollution influenced by a velocity field is described. Several approac...

Stochastic chemical systems with diffusion are modeled with a reactiondiffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reactiondiffusion master equation. The space...

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the timeand space-fractional diffusion equation with the quotient of the orders of the timeand space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then ...