Kinetic formulation of conservation laws / Benoit Perthame

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