Linearized Boltzmann equation in \(L^ 1\) space
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Publication:2545980
DOI10.1016/0022-247X(71)90231-9zbMath0216.17201MaRDI QIDQ2545980
Publication date: 1971
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Spectrum, resolvent (47A10) Equations and inequalities involving linear operators, with vector unknowns (47A50) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)
Related Items (26)
A generalization of the Vidav-Jörgens perturbation theorem for semigroups and its application to transport theory ⋮ A characterization of some subsets of Schechter's essential spectrum and application to singular transport equation ⋮ Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation ⋮ The Cauchy problem for the linear Maxwell-Boltzmann equation ⋮ Positivity and stability of the essential spectrum for singular transport semigroups with non-vacuum boundary conditions ⋮ Existence results for nonlinear mono-energetic singular transport equations: \(L^p\)-spaces ⋮ The eigenvalue spectrum of the linear Boltzmann operator in \(L^1(R^6)\) and \(L^2(R^6)\) ⋮ On substochastic C0-semigroups and their generators ⋮ Singular one-dimensional transport equations on \(L_{p}\) spaces. ⋮ Positive solution of a time and energy dependent neutron transport problem ⋮ On the linear transport equation for rigid spheres ⋮ Existence results for nonlinear mono-energetic singular transport equations: \(L_1\)-spaces ⋮ Scattering theory for linearized Boltzmann equation. Survey and new results ⋮ Relatively compact-like perturbations, essential spectra and application ⋮ The spectrum of a one-velocity transport operator with integral boundary conditions of Maxwell type ⋮ A Nonlinear Boltzmann Equation in Transport Theory ⋮ Fredholm operators, essential spectra and application to transport equations ⋮ Measures on phase space as solutions of the one-dimensional neutron transport equation ⋮ Spectral properties of a transport operator in a slab with integral boundary conditions ⋮ Solution of a nonlinear Boltzmann equation for neutron transport in L\(^1\) space ⋮ On nonlinear time-dependent multivelocity transport equations ⋮ On nonlinear neutron transport equations ⋮ Spectral properties of a streaming operator with diffuse reflection boundary condition ⋮ A stationary criticality problem in general \(L_ p\)-space for energy dependent neutron transport in cylindrical geometry ⋮ Some remarks on the Schechter essential spectrum and applications to transport equations. ⋮ Positivity in time dependent linear transport theory
Cites Work
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- Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
- Complete continuity of the free gas scattering operator in neutron thermalization theory
- Analytic properties of the inverse \(A(z)^{-1}\) of an analytic linear operator valued function \(A(z)\)
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