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Kinetic formulation of conservation laws / Benoit Perthame

Auteur principal : Perthame, Benoit, 1959-, AuteurType de document : MonographieCollection : Oxford lecture series in mathematics and its applications, 21Langue : anglais.Pays : Etats Unis.Éditeur : New York : Oxford University Press, 2002Description : 1 vol. (XI-198 p.) ; 24 cmISBN : 0198509138.Bibliographie : Bibliogr. p. [183]-196. Index.Sujet MSC : 35L65, PDEs - Hyperbolic equations and hyperbolic systems, Hyperbolic conservation laws
35L60, PDEs - Hyperbolic equations and hyperbolic systems, First-order nonlinear hyperbolic equations
35L40, PDEs - Hyperbolic equations and hyperbolic systems, First-order hyperbolic systems
35L45, PDEs - Hyperbolic equations and hyperbolic systems, Initial value problems for first-order hyperbolic systems
82C40, Time-dependent statistical mechanics, Kinetic theory of gases
En-ligne : Zentralblatt | MathScinet
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35 PER (Browse shelf) Available 02195-01

With this book, the author gives an overview of the mathematical connections between kinetic theory and conservation laws. The main advantage of such a connection is that tools from linear theory can be applied to nonlinear problems because the kinetic approach allows to rewrite the original nonlinear equation as a linear equation acting on a nonlinear quantity. Tools like Fourier transform, moment methods, and regularization by convolution can then be applied and either yield new results (like regularity or a priori bounds for the solution of the nonlinear equation), or known results are recovered with a different proof (like existence and uniqueness for scalar conservation laws). Apart from giving a new perspective on the theory of conservation laws, the author also shows how the kinetic approach can be used to construct numerical methods with interesting features. (Zentralblatt)

Bibliogr. p. [183]-196. Index

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