Author | Agoshkov, Valeri. author |
---|---|
Title | Boundary Value Problems for Transport Equations [electronic resource] / by Valeri Agoshkov |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1994-1 |
Descript | XVII, 278 p. online resource |
1 Problems and equations of transport theory -- 1.1 Some notions of transport theory -- 1.2 Basic transport equations -- 1.3 Boundary conditions and statements of problems -- 1.4 Typical boundary value problems -- 1.5 Integral equations of transport theory -- 1.6 Adjoint problems -- 1.7 Correctness of statements and need of new functional spaces -- 2 Functional spaces, existence of traces, and extension of functions -- 2.1 Spaces Hp1(? ? D). Trace existence and extensions of functions -- 2.2 Spaces Hp1[-1,1] ร (0, H). Trace existence and extensions of functions -- 2.3 Spaces of periodic functions V and Hpt + ?, k Properties of operator ? -- 2.4 Spaces Hpt + ?, k(? ร D). Existence of traces and extensions of functions -- 3 Variational statements and generalized solutions of transport problems -- 3.1 The first variational problem. Necessary and sufficient conditions of solvability in Hp1 -- 3.2 The second variational problem. Estimates of boundary values of solutions -- 3.3 General approach to symmetrization. The third variational problem. Existence of solutions -- 3.4 Reflection operators and fundamental functions -- 3.5 Existence of solutions for periodic problems -- 4 Regularity properties of generalized solutions -- 4.1 Regularity of periodic solutions in a plane-parallel geometry -- 4.2 Regularity of periodic solutions in three-dimensional geometry -- 4.3 Regularity for the boundary value plane-parallel problem -- 4.4 Three-dimensional boundary value problems -- 4.5 Regularity of solutions in (x, y)-geometry -- 5 Applications to analysis of transport problems and numerical algorithms -- 5.1 Operators L-1S, SL*-1 -- 5.2 Fundamental functions of reflection operators and inverse problems -- 5.3 Convergence of domain decomposition methods for transport problems -- 5.4 Some applications for numerical algorithms -- 5.5 Energy dependent problems -- 5.6 Justification of a perturbation algorithm for a nonlinear transport equation -- Appendix. Main notations and functional spaces