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The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
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J. Banasiak
Published/Copyright:
June 7, 2010
Abstract
In this paper we prove the existence of all moments of the solutions to the time-dependent spatially homogeneous transport equation describing elastic and inelastic scattering of particles. The proof uses the theory of resolvent positive operators and Desch's perturbation theorem. As an application we carry out the asymptotic analysis of the full transport equation with dominant elastic scattering and, using the results of the first part of the paper, we show that its solution can be approximated in the L1-norm by the solution of the limit equation obtained by formal asymptotic expansion.
Key words and phrases.: Evolution equations; positive semigroups; inelastic scattering; singular perturbations; hydrodynamic limit
Received: 1999-10-10
Revised: 2000-03-28
Published Online: 2010-06-07
Published in Print: 2000-December
© Heldermann Verlag
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- Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
- The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
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Keywords for this article
Evolution equations;
positive semigroups;
inelastic scattering;
singular perturbations;
hydrodynamic limit
Articles in the same Issue
- Category Analogue of Sup-Measurability Problem
- Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
- The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
- Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences
- Local Existence of Solutions of a Free Boundary Problem for Equations of Compressible Viscous Heat-Conducting Capillary Fluids
- Quotients of Quasi-Continuous Functions
- Integrals of Legendre Polynomials and Solution of Some Partial Differential Equations
- Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
- On Continuity of Measurable Cocycles
