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Existence of Traveling Waves of General Gray-Scott Models.
- Source :
-
Journal of Dynamics & Differential Equations . Dec2018, Vol. 30 Issue 4, p1469-1487. 19p. - Publication Year :
- 2018
-
Abstract
- 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]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 30
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 132813866
- Full Text :
- https://doi.org/10.1007/s10884-017-9603-5