The Cauchy Problem in Kinetic TheorySIAM, 01.01.1996 - 254 Seiten This clearly written, 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 (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? |
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Anal Assume Asymptotic asymptotic stability Boltzmann Equation bounded Cauchy data Cauchy Problem chapter classical solutions collision Collisionless Plasma Comm compact compute const constant convergence define Degond density dv dx dt dv dy dw du dv dx dv dy ly estimate fa(t follows function ƒ ƒ Global Existence Global Solutions hard sphere Hence Horst initial data initial value problem integral kernel Kinetic Theory L²(v Lemma linear Math Maxwell's equations Mech Meth nonnegative norm orthonormal basis P.L. Lions Particle methods Phys plasma physics Proof relativistic Vlasov-Maxwell system satisfies Similarly space symmetric Theorem variables velocity Vlasov equation Vlasov-Poisson system Weak Solutions write δε µ³