Stability of Global Solution to Boltzmann-Enskog Equation with External Force (Communications in Mathematical Research, 2021)
In the presence of external forces depending only on the time and spacevariables, the Boltzmann-Enskog equation formally conserves only the mass of thesystem, and its entropy functional is also nonincreasing. Corresponding to this typeof equation, we first give some hypotheses of its bicharacteristic equations and thenget some results about the stability of its global solution with the help of two newLyapunov functionals: one is to describe interactions between particles with differentvelocities and the other is to measure the $L^1$ distance between two mild solutions.The former Lyapunov functional yields the time-asymptotic convergence of globalclassical solutions to the collision free motion while the latter is applied into the verification of the $L^1$ stability of global mild solutions to the Boltzmann-Enskog equationfor a moderately or highly dense gas in the influence of external forces.
Keywords: Boltzmann-Enskog equation; global solution; stability; Lyapunov functional.