The Cauchy Problem in Kinetic Theory by Robert T. Glassey (PDF)

Description

This 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?

User’s Reviews

Editorial Reviews: Review ‘The book will make a very valuable addition to the bookshelf of every researcher in mathematical kinetic theory.’ Reinhard Ilner, SIAM Review Book Description This clearly written, self-contained volume studies the basic equations of kinetic theory in all of space.

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