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MARC 21

The Cauchy problem in kinetic theory
Tag	Description
020	$a9781611971477
082	$a530.1360151535
099	$aOnline Resource: Society for Industrial and Applied Mathematics
100	$aGlassey, Robert$d1946-
245	$aThe Cauchy problem in kinetic theory$h[Ebook]$cRobert T. Glassey.
260	$aPhiladelphia, Pa$bSociety for Industrial and Applied Mathematics$c1996.
300	$a1 online resource (xii, 236 pages)
440	$aOther Titles in Applied Mathematics
520	$aThis clearly written, self-contained volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term.The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated? The topics treated include the study of the Boltzmann collision operator, the study of the initial-value problem for the Boltzmann equation with “small” and “near equilibrium” data, global smooth solvability of the initial-value problem for the Vlasov-Poisson system with smooth initial data of unrestricted size, conditions under which the initial-value problem for the Vlasov-Maxwell system has global-in-time solutions (in both the smooth and weak senses), and more.
533	$aDigital reproduction.$bPhiladelphia :$cSociety for Industrial and Applied Mathematics,$d1996.$fOther Titles in Applied Mathematics$nAccess restricted to SISSA internal users ; Digital files written in PDF mode and can be read using Adobe Acrobat Reader software
538	$aOnline access to this digital book is available through World Wide Web and with IP address (only for SISSA internal users)
856	$uhttp://dx.doi.org/10.1137/1.9781611971477