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Boundary Value Problems in Abstract Kinetic Theory
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In this paper, the authors present a survey of abstract kinetic theory and its application in various areas of physics, chemistry, biology, and engineering, including radiative transfer and rarefied gas dynamics.Abstract:
This monograph is intended to be a reasonably self -contained and fairly complete exposition of rigorous results in abstract kinetic theory. Throughout, abstract kinetic equations refer to (an abstract formulation of) equations which describe transport of particles, momentum, energy, or, indeed, any transportable physical quantity. These include the equations of traditional (neutron) transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. The mathematical problems addressed within the monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The reader is assumed to have a certain familiarity with elementary aspects of functional analysis, especially basic semigroup theory, and an effort is made to outline any more specialized topics as they are introduced. Over the past several years there has been substantial progress in developing an abstract mathematical framework for treating linear transport problems. The benefits of such an abstract theory are twofold: (i) a mathematically rigorous basis has been established for a variety of problems which were traditionally treated by somewhat heuristic distribution theory methods; and (ii) the results obtained are applicable to a great variety of disparate kinetic processes. Thus, numerous different systems of integrodifferential equations which model a variety of kinetic processes are themselves modelled by an abstract operator equation on a Hilbert (or Banach) space.read more
Citations
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H1 Approximations of the Neutron Transport Equation and Associated Diffusion Equations
TL;DR: In this paper, the authors give H1 approximations of the neutron transport equation based on variational formulations of the transport equation recently presented in Bourhrara (2004) and show that the strong formulation of one of these approximate problems is no other than the classical neutron diffusion equation, taking into account the transport imposed incoming flux and the albedo boundary conditions.
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A three-dimensional Boltzmann-like model of outgassing and contamination
TL;DR: In this paper, a Boltzmann-like model of outgassing and contamination in a three-dimensional region V = V 1 ∪ V 2 ∪V 3, where V 1 is the region where the contaminant particles are produced, and V 2 is where such particles migrate and interact with some inert gas.
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Weak spectral mapping theorems for C0-groups associated to transport equations in slab geometry
TL;DR: In this paper, the C 0 -groups governing neutron transport equations with reflecting boundary conditions in slab geometry satisfy a weak spectral mapping theorem in any L p spaces 1 ⩽ p ∞.
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Asymptotic behavior of the classical time dependent solution for particle transport in a finite body with [0,vM] ENERGY
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Existence Result for the Kinetic Neutron Transport Problem in the Presence of Delayed Neutrons
Lahbib Bourhrara,Richard Sanchez +1 more
TL;DR: In this paper, a new proof of existence result concerning the kinetic neutron transport equation is proposed, which is constructive in the sense that a sequence that converges to the solution of the problem by iterating on the collision terms is constructed.
References
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Light Scattering by Small Particles
H. C. Van de Hulst,V. Twersky +1 more
TL;DR: Light scattering by small particles as mentioned in this paper, Light scattering by Small Particle Scattering (LPS), Light scattering with small particles (LSC), Light Scattering by Small Parts (LSP),
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Small amplitude processes in charged and neutral one-component systems
TL;DR: In this article, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.