Mathematical problems in collisionless kinetic theory.

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The project involves addressing certain problems in collisionless kinetic theory. Collisionless kinetic theory concerns the Vlasov equation coupled to field equations such as the Poisson equation of Newtonian gravity or electrostatics, the Maxwell equations of electromagnetism, or the Einstein equations of general relativity. The latter two are hyperbolic equations. Great progress is currently being made on the study of solutions of these equations in neighbourhoods of certain explicit stationary solutions. The aim of the project is to adapt techniques in nonlinear partial differential equations, developed over recent years, to address problems related to the asymptotic behaviour and global existence properties of solutions of these equations. The project falls under the EPSRC strategic theme of mathematical sciences, and the research areas of mathematical analysis, mathematical physics, and nonlinear systems.