Differential and Integral Equations

Dynamics of a parabolic problem arising in nuclear engineering

I. Antón and J. López-Gómez

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Abstract

This paper analyzes the dynamics of a spatially heterogeneous parabolic system, which is a refinement of a classical prototype model in Nuclear Engineering proposed by W. E. Kastenberg and P. L. Chambré [13], introduced to study the interactions between the density of fast neutrons and the temperature in the reactor. The dynamics is completely characterized within the ranges of values of the parameters where the model does not admit a positive steady state, as well as in the region where it admits a positive steady state and the system can be transformed, through an appropriate change of variable, into an irreducible cooperative system, as discussed by J. López-Gómez and M. Molina-Meyer [19], where it is shown that the coexistence state is a global attractor.

Article information

Source
Differential Integral Equations, Volume 27, Number 7/8 (2014), 691-720.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1399395749

Mathematical Reviews number (MathSciNet)
MR3200760

Zentralblatt MATH identifier
1340.35111

Subjects
Primary: 35K40: Second-order parabolic systems 35K55: Nonlinear parabolic equations 35B09: Positive solutions

Citation

Antón, I.; López-Gómez, J. Dynamics of a parabolic problem arising in nuclear engineering. Differential Integral Equations 27 (2014), no. 7/8, 691--720. https://projecteuclid.org/euclid.die/1399395749


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