On Backward Solutions Of Boltzmann Equation

Boltzmann Equation, which describes the evolution of nonequilibrium distributionfunction f (x,v,t), is one of the most important equations in nonequilibrium statisticalphysics. This paper discuss the backward solutions of initial value problem (IVP) ofspace inhomogeneous Boltzmann equation considering the inverse power potential withweak angular cut-of, and dedicates that if f0(x,v) have spatial decay properties, the globalmild solution of backward Boltzmann equation exists. This paper also gives the stabilityestimate of the long time behavior of backward solution f∞(x,v)=limtâ†'∞f (x,v,t)This paper’s innovation mainly has three points:Prove the global existence of the backward solution of IVP of space inhomoge-neous Bolzmann equationDiscuss the long time behavior f-∞(x,v) of backward solution, and give the stabilityestimate of f∞(x,v)Give the L1stability estimate of backward solution f (x,v,t)...