Spectral properties and regularity of solutions to transport equations in slab geometry

DOI10.1002/mma.767zbMath1107.47060OpenAlexW1976384300MaRDI QIDQ3418715

Khalid Latrach, Hatem Megdiche

Publication date: 24 January 2007

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.767

zbMATH Keywords

perturbation theoryboundary conditionsspectral analysisone-parameter semigroupslinear transport equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) Diffraction, scattering (78A45) Perturbation theory of linear operators (47A55) Transport processes in time-dependent statistical mechanics (82C70) Applications of operator theory to differential and integral equations (47N20) Boundary value problems for nonlinear first-order PDEs (35F30) Integro-differential operators (47G20)

Related Items (5)

Asymptotic spectrum of the linear Boltzmann equation with general boundary conditions in finite bodies ⋮ Spectral distribution of transport operator arising in growing cell populations ⋮ Time asymptotic behavior of the solution to the linear Boltzmann equation in finite bodies ⋮ On a resolvent approach for perturbed semigroups and application to \(L^1\)-neutron transport theory ⋮ Spectral analysis of transport equations with bounce-back boundary conditions

Cites Work

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• One-parameter semigroups of positive operators
• Boundary value problems in abstract kinetic theory
• Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
• Spectra of perturbed semigroups with applications to transport theory

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