Interface Development and Local Solutions to Reaction-Diffusion Equations
Ugur G. Abdulla, John R. King · SIAM Journal on Mathematical Analysis · 2000
The evolution of interfaces and the local behavior of solutions near the interface in problems for one-dimensional reaction-diffusion equations are studied. In all cases explicit formulae for the interface, with accuracy up to constant coefficients, are found together with the local solution. The methods used are matched asymptotic expansions for preliminary formal results, and rescaling and a barrier technique for rigorous proof, using special comparison theorems in irregular domains.