From Hyperbolic Systems To Kinetic Theory PDF Download
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Author | : Luc Tartar |
Publisher | : Springer Science & Business Media |
Total Pages | : 295 |
Release | : 2008-02-26 |
Genre | : Mathematics |
ISBN | : 3540775625 |
Download From Hyperbolic Systems to Kinetic Theory Book in PDF, ePub and Kindle
This fascinating book, penned by Luc Tartar of America’s Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can’t apply.
Author | : Vinicio C Boffi |
Publisher | : World Scientific |
Total Pages | : 284 |
Release | : 1992-10-28 |
Genre | : |
ISBN | : 9814554456 |
Download Nonlinear Kinetic Theory And Mathematical Aspects Of Hyperbolic Systems Book in PDF, ePub and Kindle
Contents: Mathematical Biology and Kinetic Theory Evolution of the Dominance in a Population of Interacting Organisms (N Bellomo & M Lachowicz)Formation of Maxwellian Tails (A V Bobylev)On Long Time Asymptotics of the Vlasov-Poisson-Boltzmann System (J Dolbeault)The Classical Limit of a Self-Consistent Quantum-Vlasov Equation in 3-D (P A Markowich & N J Mauser)Simple Balance Methods for Transport in Stochastic Mixtures (G C Pomraning)Knudsen Layer Analysis by the Semicontinuous Boltzmann Equation (L Preziosi)Remarks on a Self Similar Fluid Dynamic Limit for the Broadwell System (M Slemrod & A E Tzavaras)On Extended Kinetic Theory with Chemical Reaction (C Spiga)Stability and Exponential Convergence in Lp for the Spatially Homogeneous Boltzmann Equation (B Wennberg)and other papers Readership: Applied mathematicians. keywords:Proceedings;Workshop;Rapallo (Italy);Kinetic Theory;Hyperbolic Systems;Nonlinear Kinetic Theory
Author | : B. Perthame |
Publisher | : World Scientific |
Total Pages | : 232 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9789810216719 |
Download Advances in Kinetic Theory and Computing Book in PDF, ePub and Kindle
This selection of 8 papers discusses ?Equations of Kinetic Physics? with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations ? Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) ? Followed by a survey of kinetic and macroscopic models for semiconductor devices ? Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics ? Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) ? followed by two papers on the analysis and numerical analysis of the Boltzmann equations ? Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).
Author | : Benoit Perthame |
Publisher | : World Scientific |
Total Pages | : 228 |
Release | : 1994-09-30 |
Genre | : Mathematics |
ISBN | : 9814502332 |
Download Advances In Kinetic Theory And Computing : Selected Papers Book in PDF, ePub and Kindle
This selection of 8 papers discusses “Equations of Kinetic Physics” with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations — Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) — Followed by a survey of kinetic and macroscopic models for semiconductor devices — Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics — Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) — followed by two papers on the analysis and numerical analysis of the Boltzmann equations — Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).
Author | : Philippe G. LeFloch |
Publisher | : Springer Science & Business Media |
Total Pages | : 1010 |
Release | : 2002-07-01 |
Genre | : Mathematics |
ISBN | : 9783764366872 |
Download Hyperbolic Systems of Conservation Laws Book in PDF, ePub and Kindle
This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
Author | : Howard E. Conner |
Publisher | : |
Total Pages | : 20 |
Release | : 1970 |
Genre | : Differential equations, Hyperbolic |
ISBN | : |
Download Some General Properties of a Class of Semilinear Hyperbolic Systems Analogous to the Differential-integral Equations of Gas Dynamics Book in PDF, ePub and Kindle
Author | : Robert T. Glassey |
Publisher | : SIAM |
Total Pages | : 246 |
Release | : 1996-01-01 |
Genre | : Science |
ISBN | : 0898713676 |
Download The Cauchy Problem in Kinetic Theory Book in PDF, ePub and Kindle
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 together. Although describing very different phenomena, these equations share the same streaming term.
Author | : Toyoki Koga |
Publisher | : Pergamon |
Total Pages | : 324 |
Release | : 1970 |
Genre | : Science |
ISBN | : |
Download Introduction to Kinetic Theory Stochastic Processes in Gaseous Systems Book in PDF, ePub and Kindle
Author | : Luc C. Tartar |
Publisher | : |
Total Pages | : 32 |
Release | : 1980 |
Genre | : Differential equations, Hyperbolic |
ISBN | : |
Download Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable Book in PDF, ePub and Kindle
We study semilinear hyperbolic systems with quadratic nonlinearities which originate in the kinetic theory of gas as a simplification of Boltzmann's equation. Local existence is well known for these equations and the main problem is to prove global existence for nonnegative bounded data. Except for the unrealistic case where a bounded invariant region exists, no result of this type is known in three space dimensions. As in all preceding results, based on the work of Mimura-Nishida and Crandall-Tartar, we restrict ourselves to one space dimension. We show global existence for a quite general class of systems and under some special condition (S) we obtain information on the asymptotic behaviour and on scattering when the data have small L1 norm. The new idea lies in the introduction of some functional spaces where some products can be defined; this enables us to define an appropriate notion of solution in L1 and then use it to obtain local and global existence for data in L1 (R).
Author | : Robert T. Glassey |
Publisher | : SIAM |
Total Pages | : 254 |
Release | : 1996-01-01 |
Genre | : Science |
ISBN | : 9781611971477 |
Download The Cauchy Problem in Kinetic Theory Book in PDF, ePub and Kindle
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 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.