Differential and Integral Equations

Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability

Anthony W. Leung and Beatriz Villa

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Abstract

We consider a system of reaction-diffusion equations describing the dynamics of fission reactors with temperature feedback. There are $m$ equations for the neutrons in $m$ energy groups and a last temperature equation. We use the bifurcation method to find positive steady-states for the system which is not symmetric. We then analyze the linearized stability of the steady-state as a solution of the full system of $m+1$ parabolic equations. The asymptotic stability of the steady-state solution is proved by means of a stability theorem for sectorial operators.

Article information

Source
Differential Integral Equations, Volume 10, Number 4 (1997), 739-756.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367438639

Mathematical Reviews number (MathSciNet)
MR1741770

Zentralblatt MATH identifier
0892.35023

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations 82D75: Nuclear reactor theory; neutron transport

Citation

Leung, Anthony W.; Villa, Beatriz. Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability. Differential Integral Equations 10 (1997), no. 4, 739--756. https://projecteuclid.org/euclid.die/1367438639


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