Boundary value problems in abstract kinetic theory
This monograph presents a rigorous exposition of boundary value problems for an extensive class of kinetic equations. These equations describe the transport of particles, momentum, energy, etc. They include the equations of neutron transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. Many new results, developed since 1982, are covered in this monograph. The mathematical problems addressed within this monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The basic assumption underlying all kinetic equations studied in this monograph is that the particle flux of radiation does not interact with itself in a many-body sense, but only with the given host medium or with its own thermal equilibrium distribution in a perturbative way, and with the boundary under a linear reflection law. That is to say, only linear or linearized equations are treated. The monograph was intended to be self-contained, and specialized topics in analysis, as well as the physical background of examples, are outlined as they are introduced. The presentation comprises 13 chapters in 479 pages, followed by an extensive bibliography of 407 references.
scientific article; zbMATH DE number 4013113