Existence Of Traveling Waves Of General Gray-Scott Models

Keywords

Bounded speed set; Existence; General Gray-Scott model; Traveling wave

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.

Publication Date

12-1-2018

Publication Title

Journal of Dynamics and Differential Equations

Volume

30

Issue

4

Number of Pages

1469-1487

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10884-017-9603-5

Socpus ID

85024486079 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85024486079

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