Periodic solutions to systems of reaction-diffusion equations

✍ Scribed by Gerald Rosen

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 365 KB
• Volume: 301
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(76)90015-6

✦ Synopsis

In this paper, necessary and suficient conditions are derived for the existence of temporally periodic "dissipative structure" solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction--diffusion equations hi/at = Di V2 ci + Qi(c), where the enumerator index i runs 1 to n, ci = c*(x, t) denotes the concentration or density of the ith participating molecular or biological species, Di is the diffusivity constant for the ith species and Qi(c), an algebraic function of the n-tuple c = (cl,..,, c,), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.