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• 1
Electronic Resource
Springer
Annali di matematica pura ed applicata 106 (1975), S. 353-374
ISSN: 1618-1891
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Description / Table of Contents: Sunto Si studia una classe di moti magnetoidrodinamici alla Couette-Benard di una miscela fluida binaria in uno strato piano obliquo e, con le tecniche della teoria dei semigruppi di trasformazioni lineari limitate, si dimostra, in un opportuno spazio di Banach, l’esistenza e l’unicità della soluzione del problema di evoluzione per perturbazionifinite e l’incondizionata stabilità asintotica in norma di tali moti.
Notes: Summary We study a class of Couette-Benard M.H.D. flows of a binary mixture in a plane slant layer. By using the theory of semigroups of linear bounded transformations, we prove that the initial-value problem forfinite perturbations has one and only one solution belonging to a suitable Banach space. Finally, we show the inconditionated asymptotical stability in norm of such a solution.
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• 2
Electronic Resource
Springer
ISSN: 1618-1891
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Description / Table of Contents: Summary We study a non-linear neutron transport problem in a homogeneous slab with temperature feedback. By using some standard techniques from the theory of non-linear evolution equations, we prove existence and uniqueness of a strong solution u=u(t) at any t ∈ [0, $$\bar t$$ ]. Finally, we indicate a procedure to find a non-negative continuous b=b(t), such that ‖u(t)‖⩽b(t), at any t ∈ [0, $$\bar t$$ ].
Notes: Riassunto. Si studia un problema non lineare di trasporto di neutroni in un muro omogeneo con sezioni d'urto dipendenti dalla temperatura. Facendo uso di alcune tecniche standard della teoria delle equazioni non lineari di evoluzione, si prova l'esistenza e l'unicità di una soluzione forte u=u(t), per ogni t ∈ [0, $$\bar t$$ ], ove $$\bar t$$ è scelto in modo opportuno. Infine, si indica un procedimento per determinare una funzione continua e non negativa b=b(t), tale che ‖u(t)‖⩽b(t) per ogni t ∈ [0, $$\bar t$$ ].
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• 3
Electronic Resource
Springer
Annali di matematica pura ed applicata 170 (1996), S. 359-376
ISSN: 1618-1891
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Summary We study a new one-parameter family of linear bounded operators Y(t), t⩾O which is uniquely defined by a linear operator A, not necessarily bounded, and by a linear bounded operator B. The definition of Y(t), t ⩾ 0 given in Section 2 was suggested by a particle transport problem with multiplying boundary conditions.
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• 4
Electronic Resource
Chichester, West Sussex : Wiley-Blackwell
ISSN: 0170-4214
Keywords: Mathematics and Statistics ; Applied Mathematics
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Mathematics
Notes: We show that the free streaming operator with diffusive multiplying boundary conditions is the generator of a quasi-bounded semigroup. We also examine some spectral properties of such an operator.
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• 5
Electronic Resource
Chichester, West Sussex : Wiley-Blackwell
ISSN: 0170-4214
Keywords: Engineering ; Numerical Methods and Modeling
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Mathematics
Notes: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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• 6
Electronic Resource
Chichester, West Sussex : Wiley-Blackwell
ISSN: 0170-4214
Keywords: Mathematics and Statistics ; Applied Mathematics
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Mathematics
Notes: We study a mathematical model of neutron multiplication in a slab S, by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2a of S is time dependent because of temperature variations due to the energy released by fissions.Starting from a quite detailed picture of the physical phenomena occurring in S, we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂(t), for the total number of precursors Ĉ = Ĉ(t), and for the half-thickness of S, a = a(t).We finally examine some stability properties of such a system of ordinary differential equations.
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• 7
Electronic Resource
Chichester, West Sussex : Wiley-Blackwell
ISSN: 0170-4214
Keywords: Mathematics and Statistics ; Applied Mathematics
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Mathematics
Notes: We consider a Boltzmann-like model of a problem of outgassing and contamination in a region R. For simplicity, we assume that R = R1 ∪ R2 ∪ R3, where R1 is the slab {x: -a 〈 x 〈 0}, R2 = {x:0 〈 x 〈 b}, R3 = {x: b 〈 x 〈 b1}. R1 is the region where the contaminant particles are produced, R2 is the ‘cavity’ where such particles migrate and interact with some inert gas, usually at low pressure, and R3 is the region which is contaminated by the particles coming from R2. In each of the three regions, the behaviour of the contaminant particles is represented by means of a Boltzmann-like equation.We prove that such a mathematical problem has a unique positive strict solution, belonging to a suitable Banach space Y. A system of ordinary differential equations is also derived, which gives the global balances of the contaminant particles in each of the three regions.
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• 8
Electronic Resource
Springer
Astrophysics and space science 234 (1995), S. 85-105
ISSN: 1572-946X
Source: Springer Online Journal Archives 1860-2000
Topics: Physics
Notes: Abstract We consider time dependent photon transport in a three dimensional interstellar cloud which occupies a three dimensional regionV. One or more clumps of given shapes are present withinV and their positions are determined by a suitable set of stochastic variables. Iff is the photon number density in the cloud or in the clumps, then our mathematical model leads to two coupled initial value problems for the average photon density over the stochastic variables 〈f〉 and forf * =f -〈f〉. By using the theory of semigroups, we prove existence and uniqueness of a strongly continuous solution and examine the small fluctuation approximation of such a solution.
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• 9
Electronic Resource
College Park, Md. : American Institute of Physics (AIP)
Journal of Mathematical Physics 37 (1996), S. 2815-2823
ISSN: 1089-7658
Source: AIP Digital Archive
Topics: Mathematics , Physics
Notes: The free streaming operator T is considered in a convex three dimensional region V, with diffusive multiplying boundary conditions. Some mathematical properties of T are examined by writing the particle density as an infinite series which takes into account successive reflections on ∂V, and by introducing an operator which in some sense annihilates the multiplying effect of ∂V. © 1996 American Institute of Physics.
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