Exact static nonequilibrium patterns in a fractional diffusion--reaction system

MARCELO SANDKOVSKY, MIGUEL A. BENAVENTE Y ROBERTO R. DEZA

Rosario

Congreso; II MACI 2009; 2009

ASAMACI

We report on the analytical finding of exact static nonequilibrium patterns in a model fractional diffusion– reaction equation on a bounded domain. The original equation—equivalent to a continuous-time random-walk description of an anomalous diffusion–reaction model system—is converted into a spatially fractional diffusion–reaction equation. The fact that the domain is bounded allows to use the Laplace transform method when the (spatial) fractional derivatives are defined in the sense of Caputo. The nonequilibrium patterns so obtained are a key piece of information that—together with the formalism of nonequilibrium potential—provide a possible explanation of the ubiquitousness of normal diffusion.