Mathematical Topics in Neutron Transport Theory: New Aspects (Series on Advances in Mathematics for Applied Sciences)

This text deals with the mathematical and statistical techniques underlying the models used to understand the population dynamics of not only HIV/AIDS, but also of other infectious diseases. Attention is given to the development of strategies for the prevention and control of the international epidemic within the frameworks of the models. The text incorporates stochastic and deterministic formulations within a unifying conceptual framework 1. Introduction -- 2. Compactness properties of perturbed c0-semigroups. 2.1. Introduction. 2.2. On essential type of c0-semigroups. 2.3. On the strong convex compactness property. 2.4. Compactness properties of perturbed seroigroups. 2.5. On the stability of the essential type. 2.6. Comments -- 3. Regularity of velocity averages. 3.1. Introduction. 3.2. Stationary problems. 3.3. Evolution problems. 3.4. Comments -- 4. Spectral analysis of transport equations. A unified theory. 4.1. Introduction. 4.2. Stationary problems. 4.3. Evolution problems in Lp(symbol). 4.4. Evolution problems in L1. 4.5. The effects of delayed neutrons. 4.6. Comments -- 5. On the leading eigenelements of transport operators. 5.1. Introduction. 5.2. Spectral properties of positive operators. 5.3. The irreducibility of transport semigroups. 5.4. A general existence result. 5.5. A spectral inequality. 5.6. Nonexistence results. 5.7. Existence results. 5.8. Strict monotonicity properties of the leading eigenvalue. 5.9. Domain derivative of the leading eigenvalue. 5.10. An approximation theory of the leading eigenelements. 5.11. The criticality eigenvalue problem. 5.12. The effects of delayed neutrons. 5.13. Comments -- 6. Spectral theory of transport operators with form positive collision operators. 6.1. Introduction. 6.2. Self-adjointness and quadratic form. 6.3. Existence results for given spatial domains. 6.4. Existence results for large spatial domains. 6.5. The isotropic models. 6.6 Comments -- 7. On Miyadera perturbations of co-semigroups. 7.1. Introduction. 7.2. A perturbation theorem. 7.3. The essential type of Miyadera perturbations. 7.4. Comments -- 8. On resolvent positive operators and positive c0-semigroups. 8.1. Introduction. 8.2. A preliminary result. 8.3. Miyadera perturbations in L1(symbol) spaces. 8.4. Alternative proof of Desch's theorem. 8.5. Comments -- 9. On singular neutron transport equations in Ll spaces. 9.1. Introduction. 9.2. Generation results. 9.3. The essential type of the perturbed semigroup. 9.4. Comments -- 10. Stochastic formulations of neutron transport. Nonlinear problems. 10.1. Introduction. 10.2. Preliminary results. 10.3. Marimal solution of the stationary problem. 10.4. The subcritical case. 10.5. The critical case. 10.6. The supercritical case. 10.7. On the uniqueness. 10.8. The time dependent problem. 10.9. Time asymptotic behaviour. 10.10. Comments -- 11. Velocity averages and inverse problems. 11.1. Introduction. 11.2. One dimensional inverse problems. 11.3. Multidimensional inverse problems. 11.4. The dimension two. 11.5. Characterization of the range of integrated fluxes. 11.6. Comments -- 12. Limiting absorption principles and wave operators in L1([symbol]) spaces with applications to transport theory. 12.1. Introduction. 12.2. Preliminary results. 12.3. On the wave operators. 12.4. The similarity of T0 and T. 12.5. Converse results. 12.6. Scattering theory for transport operators. 12.7. Comments -- 13. Lin's factorization formalism and applications to transport theory. 13.1. Introduction. 13.2. A preliminary result. 13.3. On the wave operator s lim[symbols]. 13.4. Application to transport groups. Part 1. 13.5. Application to transport groups. Part 2. 13.6. Comments -- 14. Inverse scattering and albedo operator / M. Choulli and P. Stefanov 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. 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 c 0 -semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c 0 -semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport ope This volume presents mathematical developments on the subject of neutron transport equations. Several different themes are dealt with including regularity of velocity averages, spectral analysis, and inverse problems arising in the stochastic theory of neutron chain fissions.