Differential and Integral Equations
- Differential Integral Equations
- Volume 10, Number 4 (1997), 739-756.
Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability
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.
Differential Integral Equations, Volume 10, Number 4 (1997), 739-756.
First available in Project Euclid: 1 May 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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