6 edition of The Cauchy Problem in Kinetic Theory found in the catalog.
January 1, 1987
by Society for Industrial Mathematics
Written in English
|The Physical Object|
|Number of Pages||253|
Solve the Cauchy problem u t +uu x =0, u(x,0)= h(x). () The characteristic equations are dx dt = z, dy dt =1, dz dt =0, and Γ may be parametrized by (s,0,h(s)). x = h(s)t+s, y = t, z = h(s). u(x,y)=h(x−uy) () The characteristic projection in the xt-plane1 passing through the point (s,0) is the line. The solution of the Cauchy problem can be written as The existence and uniqueness of the solution for any fixed ε >0 and real k follows from the general theory of semi-groups under very general restrictions on the scattering cross-section in the Boltzmann collision integral (see [ 24 ] for potentials with compact support and [ 27 ] for the.
Baron Augustin-Louis Cauchy FRS FRSE (/ k oʊ ˈ ʃ iː /; French: [oɡystɛ̃ lwi koʃi]; 21 August – 23 May ) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum was one of the first to state and rigorously prove theorems of calculus, rejecting the. The subject and history of the mechanics of inhomogeneous media are briefly reviewed with emphasis on the new theoretical approaches developed by Maxwell and Boltzmann. In particular, attention is given to the theoretical fundamentals of the mechanics of inhomogeneous media, derivation of the Boltzmann kinetic equation, a new method for solving the Boltzmann equation, and the Cauchy problem.
The theory underlying the discussion is the general theory of relativity. Moreover, in the book, matter is modelled using kinetic theory. As background material, the general theory of the Cauchy problem for the Einstein–Vlasov equations is therefore developed. His book “The Cauchy problem in kinetic theory (SIAM )” remains a fundamental textbook in the field. Although Bob was already retired when I came to Indiana for my graduate study, he kindly participated and generously offered valuable guidances in a working seminar that I ran on the DiPerna-Lions theory for Boltzmann equations in the.
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This book stems from lecture notes for a course in Kinetic Theory I gave at Indiana University in the spring of The class was composed of several of my colleagues from the faculty and advanced graduate students, most of whom were writing theses in partial differential equations.
Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems by: The Cauchy Problem in Kinetic Theory.
Title Information. Published: Book Code: OT Pages: xii + 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.
Get this from a library. The Cauchy problem in kinetic theory. [Robert Glassey; Society for Industrial and Applied Mathematics.] -- This 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. The book by Glassey  is a good reference for the general subject of the Cauchy problem in kinetic theory (in particular for the Vlasov–Poisson and Vlasov–Maxwell equations, and for the Boltzmann equation near equilibrium).
Journals & Books; Register Sign in. Sign Advanced. Journal of Differential Equations. VolumeIs 15 MayPages Cauchy problem for the ellipsoidal BGK model for polyatomic particles. Author links open overlay panel Sa Jun Park Seok-Bae Yun.
Show more. https: Kinetic theory of gases. Cauchy problem. Recommended. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.
Contents: On the Cauchy Problem for the Boltzmann Equation (L Arlotti & N Bellomo). This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable.
The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Chapter 1 describes models and problems, Chapter 2 is about the theory of the Cauchy problem (including regularity and estimates on solutions), Chapter 3 enters into the links and analogies between kinetic theory and information theory, Chapter 4 is concerned with.
Well-posedness of Cauchy problem for Landau equation in critical Besov space. Kinetic & Related Models,12 (4): doi: /krm The book is essentially devoted to analytic aspects and deals with the analysis of the Cauchy problem and with the development of an asymptotic theory to obtain the macroscopic description from the mesoscopic one.
Sample Chapter(s) Chapter 1: From the Boltzmann Equation to the Averaged Boltzmann Equation (1, KB) Request Inspection Copy. The Cauchy problem in kinetic theory. [Robert Glassey] Home. WorldCat Home About WorldCat Help.
Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create Book\/a>, schema:CreativeWork\/a> ; \u00A0\u00A0\u00A0\n library. The existence and uniqueness result is obtained by an application of the theory of ODEs in Banach spaces , that has been successfully used in many frameworks, such as mixture setting , polymers kinetic problems , quantum Boltzmann equation for bosons in very low temperature  and the weak wave turbulence models for stratiﬁed.
The cauchy problem for the Boltzmann equation. A survey of recent results. Spohn, Herbert. Preview Buy Chap95 € A nonlinear half-space problem in the kinetic theory of gases.
Pages Ytrehus, Tor. Book Title Kinetic Theories and the Boltzmann Equation. The BGK model and the ES-BGK model of the Boltzmann equation are of great importance in the kinetic theory of rarefied gases. For the Cauchy problems with general initial data, smooth solutions.
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition) or it can be either of is named after Augustin Louis Cauchy.
Cercignani C. () Hyperbolic Problems in Kinetic Theory. In: Donato A., Oliveri F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol The Cauchy problem for the inhomogeneous porous medium equation.
Networks & Heterogeneous Media,1 (2): doi: /nhm  Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation.
Session “Statistical Mechanics, Kinetics and Quantum Theory of Condensed Matter” Published: 26 November ; The cauchy problem for BBGKY hierarchy of quantum kinetic equations with coulomb potential.
Brokate 1 &. ON THE CAUCHY PROBLEM FOR THE PRESSURELESS EULER–NAVIER–STOKES SYSTEM IN THE WHOLE SPACE YOUNG-PIL CHOI AND JINWOOK JUNG Abstract. In this paper, we study the global Cauchy problem for a two-phase ﬂuid model consisting of the pressureless Euler equations and the incompressible Navier–Stokes equations where the coupling of two.
The Cauchy Problem in Kinetic Theory by Robert T. Glassey Book Resume: Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations.BOOKS Numerical Computation Using C.
Academic Press, Boston, MA. Errata. Support programs to accompany the book The Cauchy Problem in Kinetic Theory. SIAM, Philadelphia, CPKT_Errata. Details. SELECTED RESEARCH PAPERS. On the blowing-up of solutions to the Cauchy Problem for nonlinear Schroedinger equations. J. Math. Phys. 18 ( In the non-singular case, namely µ > 0, weak solutions are know to be strong under the periodic boundary condition, see , and for the Cauchy problem Ω = .