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Many-Particle Dynamics and Kinetic Equations (Hardcover, 1997 ed.)
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Many-Particle Dynamics and Kinetic Equations (Hardcover, 1997 ed.)
Series: Mathematics and Its Applications, 420
Expected to ship within 10 - 15 working days
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As our title suggests, there are two aspects in the subject of this
book. The first is the mathematical investigation of the dynamics
of infinite systems of in teracting particles and the description
of the time evolution of their states. The second is the rigorous
derivation of kinetic equations starting from the results of the
aforementioned investigation. As is well known, statistical
mechanics started in the last century with some papers written by
Maxwell and Boltzmann. Although some of their statements seemed
statistically obvious, we must prove that they do not contradict
what me chanics predicts. In some cases, in particular for
equilibrium states, it turns out that mechanics easily provides the
required justification. However things are not so easy, if we take
a step forward and consider a gas is not in equilibrium, as is,
e.g., the case for air around a flying vehicle. Questions of this
kind have been asked since the dawn of the kinetic theory of gases,
especially when certain results appeared to lead to paradoxical
conclu sions. Today this matter is rather well understood and a
rigorous kinetic theory is emerging. The importance of these
developments stems not only from the need of providing a careful
foundation of such a basic physical theory, but also to exhibit a
prototype of a mathematical construct central to the theory of
non-equilibrium phenomena of macroscopic size."
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