Stability Analysis of Nonlinear Space Dependent Reactor Kinetics

Kastenberg, W.E.

doi:10.1016/b978-0-12-029305-6.50008-x

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2005

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Cited by 8 publications

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“…Equation (1.1) can be derived as a simple model for neutron diffusion (feedback control of nuclear reactor) [27,56]. In this case φ (which must be nonnegative) and σ stand for the neutron flux and neutron diffusion respectively.…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence

Karachalios

Zographopoulos

2005

Calc. Var.

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We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary states, covering both the cases of a bounded and an unbounded domain. The global bifurcation of stationary states, implies-in conjuction with the definition of a gradient dynamical system in the natural phase space-that at least in the case of a bounded domain, any solution with nonnegative initial data tends to the trivial or the nonnegative equilibrium. Applications of the global bifurcation result to general degenerate semilinear as well as to quasilinear elliptic equations, are also discussed.

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Section: Introductionmentioning

confidence: 99%