Existence of Traveling Waves of General Gray-Scott Models.

This work gives a rigorous proof of the existence of propagating traveling waves of a nonlinear reaction-diffusion system which is a general Gray-Scott model of the pre-mixed isothermal autocatalytic chemical reaction of order m (m>1) between two chemical species, a reactant A and an auto-catalyst B, A+mB→(m+1)B, and a super-linear decay of order n>1, B→C, where 1<n<m. Here C is an inert product. Moreover, we establish that the speed set for existence must lie in a bounded interval for a given initial value u0 at -∞. The explicit bound is also derived in terms of u0 and other parameters. The same system also appears in a mathematical model of SIR type in infectious diseases. [ABSTRACT FROM AUTHOR]