Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Stability of travelling waves for a three -component reaction -diffusion system
This paper investigates a reaction-diffusion system modeling three competing species, with diffusion in one space dimension. The main result is the existence and asymptotic stability of a travelling wave connecting two stable equilibria. The results are obtained in a small parameter regime where two of the species diffuse very slowly. Singular perturbation methods are used to locate the connecting solution, and the existence for positive values of the perturbation parameter is established via the connection index of Conley. The stability result applies geometric and topological methods developed by Alexander, Gardner, and Jones, to the analysis of the linearized equations about the travelling wave. This paper addresses some of the difficulties in extending these existence and stability methods to systems of more than two equations. ^
Miller, Patrick David, "Stability of travelling waves for a three -component reaction -diffusion system" (1994). Doctoral Dissertations Available from Proquest. AAI9510507.