The Cauchy Problem in Kinetic Theory

This self-contained volume studies the basic equations of kinetic theory in all of space. It contains recent 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 book has the advantage of treating 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?