Maria Villarreal, University of Central Florida


Study of Minimal Speed of Travelling Wave Solutions of Reaction Diffusion Systems Modeling Autocatalysis.

Abstract: We study the PDE system modeling cubic case (n=2) of the isothermal autocatalytic system A+nB->n+1B involving two chemical species, a reactant A and an autocatalyst B with unequal diffusion rates DA and DB. A very important aspect of the study to such underlying PDE system. Recently, bounds v* and v*dependent on D=DBDA have been found such that a minimum speed vmin exists within the bounds (v*, v*). Specifically, for the case where D > 1, we have vmin satisfy the estimates D2≤vmin &le D1+1D . From the experience from special case D=1, we have noted the importance of minimum speed Travelling Fronts to the determination of the spread of general initial disturbances. For various diffusion rates D≥1, we have computationally determined more accurate estimates for minimum speeds. This, we hope, will lead to development of new methods for analytical approach to derive more precise bounds of minimum speeds.

Advisor: Yuanwei Qi (University Central Florida)