by M Mokhtar-Kharroubi (Université de Franche-Comté, Besançon, France)

This book presents some recent mathematical developments about neutron transport equations. Several different topics are dealt with including regularity of velocity averages, spectral analysis of transport operators, inverse problems, nonlinear problems arising in the stochastic theory of neutron chain fissions, compactness properties of perturbed of c₀-semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c₀-semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport operators and their approximation, scattering theory. Besides the new problems addressed in this book a unification and extension of the classical spectral analysis of neutron transport equations is given.

• Compactness Properties of Perturbed c₀-Semigroups
• Regularity of Velocity Averages
• Spectral Analysis of Transport Equations. A Unified Theory
• On the Leading Eigenelements of Transport Operators
• Spectral Theory of Transport of Operators with Form Positive Collision Operators
• On Miyadera Perturbations of c₀-Semigroups
• On Resolvent Positive Operators and Positive c⁰-Semigroups in L¹(μ) Spaces
• On Singular Neutron Transport Equations in L1 Spaces
• Stochastic Formulations of Neutron Transport. Nonlinear Problems
• Velocity Averages and Inverse Problems
• Limiting Absorption Principles and Wave Operators in L¹(μ) Spaces with Applications to Transport Theory
• Lin's Factorization Formalism and Applications to Transport Theory
• Inverse Scattering and Albedo Operator