M. Anita,Rajani. P,



Vlasov equation,Landau dampin,functional spaces,Semi Lagrangian Schemes,


The main intention of this paper was to deliver some of the distinctive features of the Vlasov equation and Landau damping from the perspective of mathematical physics. The main thrust can be reviewed as; Vlasov equation is understood from the origin point of view. The mean field is limit of the classical Nbody problem, is depicted in pure mathematical and also statistical guidelines. We also axiomatically concluded that the Vlasov equation is completely justified as one major source that led to numeral of open problems in mathematical physics: either from molecular chaos to the problems of kinetic theory. We have delivered the mathematics of the Vlasov equations: particularly the traditional partial differential equation analysis in the functional spaces. The problem is observed to be converted as a general transport equation and relaying on the well-posedness of the equation and preserving the transport structure the Vlasov equation is solved for pivotal analytic solutions and compared with the computational solution obtained using solver codes. The analysis of the Vlasov-Poisson equation and its qualitative properties and are focused on the mathematical aspects. In this paper Landau damping is identified numerically for 1D model of non relativistic Vlasov equation.


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