A Stefan Problem for Multidimensional Reaction-Diffusion Systems
Avner Friedman, Bei Hu · SIAM Journal on Mathematical Analysis · 1996
This paper deals with a Stefan problem for a system of three weakly coupled semilinear parabolic equations. This system describes the dissolution of a particle in a solution. The dissolved species A reacts chemically with species B already in the solution, thereby forming species C. Species C diffuses in the solution and some of it adsorbs to the particle’s boundary and causes either (i) a decrease in the dissolution rate or (ii) an increase in the dissolution rate. It is proved that for the model in case (i) the solution is unstable in any small time interval, whereas for the model in case (ii), the problem has a unique solution in a small time interval.