A spectral, mapping theorem for the exponential function in ltnear transport theory

DOI10.1080/00411458508211697zbMath0613.45014OpenAlexW1998846607MaRDI QIDQ4720202

Peter Takáč

Publication date: 1985

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00411458508211697

zbMATH Keywords

perturbation theorysemigroupsasymptotic behaviourgrowth boundspectral mapping theoremweakly compactneutron transport equationpositive operators on Banach lattices

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Groups and semigroups of linear operators (47D03) Transport processes in time-dependent statistical mechanics (82C70) Integral operators (45P05) Linear operators on ordered spaces (47B60)

Related Items (21)

Spectral theory of neutron transport semigroups with partly elastic collision operators ⋮ Compactness properties for linear transport operators with abstract boundary conditions in slab geometry ⋮ Spectral Interpolation of the Linear Boltzmann Operator inL^pSpaces ⋮ Asymptotic spectrum of the linear Boltzmann equation with general boundary conditions in finite bodies ⋮ Description of the real point spectrum for a class of neutron transport operators ⋮ On the asymptotic spectrum of a transport operator with elastic and inelastic collision operators ⋮ A generalization of the Vidav-Jörgens perturbation theorem for semigroups and its application to transport theory ⋮ Spectral Theory for Neutron Transport ⋮ Time asymptotic behaviour for linear transport equations with abstract boundary conditions in slab geometry ⋮ Time asymptotic behavior of the solution to the linear Boltzmann equation in finite bodies ⋮ Some spectral properties in Banach spaces and application to transport theory ⋮ Existence results for nonlinear mono-energetic singular transport equations: \(L_1\)-spaces ⋮ The spectrum of a one-velocity transport operator with integral boundary conditions of Maxwell type ⋮ Distributed parameter systems governed by linear transport equations ⋮ Some notes on the spectral properties of C_osemigroups generated by linear transport operators ⋮ A compactness result for perturbed semigroups and application to a transport model ⋮ On \(L^1\) exponential trend to equilibrium for conservative linear kinetic equations on the torus ⋮ Some fixed point theorems in Banach spaces and application to a transport equation with delayed neutrons ⋮ Spectral analysis of transport equations with bounce-back boundary conditions ⋮ Optimal spectral theory of the linear Boltzmann equation ⋮ Two counterexamples to the spectral mapping theorem for semigroups of positive operators

Cites Work

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• Positivity in time dependent linear transport theory
• A perturbation theorem for the essential spectral radius of strongly continuous semigroups
• Über das Spektrum positiver Generatoren
• Spectral methods in linear transport theory
• A survey of the theory of spectral operators

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