Boundary Value Problems for Transport Equations

AvValeri Agoshkov

Inbunden, Engelska, 1998

Del i serien Modeling and Simulation in Science, Engineering and Technology

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Beskrivning

This text develops a functional approach for boundary value problems and includes the following components; the introduction of special functional spaces; the definition of spaces for boundary values; the analysis of the problems of trace existence; and the extension of functions with preservation of classes of regularity. This approach proves the existence of generalized solutions to problems concerned on the basis of those functional spaces introduced and also proper variational formulations of problems. The book also presents various applications of the theory developed.

Produktinformation

Utgivningsdatum:1998-09-29
Mått:155 x 235 x 20 mm
Vikt:590 g
Format:Inbunden
Språk:Engelska
Serie:Modeling and Simulation in Science, Engineering and Technology
Antal sidor:278
Upplaga:1998
Förlag:Birkhauser Boston Inc
ISBN:9780817639860

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Innehållsförteckning

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] × (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(? × 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 fornumerical algorithms.- 5.5 Energy dependent problems.- 5.6 Justification of a perturbation algorithm for a nonlinear transport equation.- Appendix. Main notations and functional spaces.