Global bifurcation diagrams of steady-states for a parabolic model related to a nuclear engineering problem

Pages: 21 - 30, Issue special, November 2013

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Inmaculada Antón - Departamento de Matemática Aplicada, Escuela Universitaria de Estadística, Universidad Complutense de Madrid, 28040 Madrid, Spain (email)
Julián López-Gómez - Departamento de Matematica Aplicada, Facultad de Ciencias Matematicas, Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040-MADRID, Spain (email)

Abstract: This paper studies the existence of coexistence states in a spatially heterogeneous reaction diffusion system arising in nuclear dynamics. Essentially, it establishes the existence of an unbounded component $\mathfrak{C}_+$ of the set of coexistence states of the system bifurcating from the trivial steady state solution, and it characterizes the values of the parameters where $\mathfrak{C}_+$ bifurcates from the trivial solution and from infinity. Throughout this paper, by a component it is meant a closed and connected subset which is maximal for the inclusion.

Keywords:  Coexistence states, global bifurcation diagrams, bifurcation from infinity, nuclear dynamics, non-cooperative systems.
Mathematics Subject Classification:  35J57, 35J25, 35Q99.

Received: August 2012;      Revised: May 2013;      Published: November 2013.