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logistic equation
Uniform $L^p$-stability theory for the space-inhomogeneous Boltzmann equation with external forces
In this paper, we present an $L^p$-stability theory for the
space-inhomogeneous Boltzmann equation with cut-off and inverse
power law potentials, when initial data are sufficiently small and
decay fast enough in phase space. For moderately soft potentials, we
show that classical solutions depend Lipschitz continuously on the
initial data in weighted $L^p$-norm. In contrast for hard
potentials, we show that classical solutions depend Hölder
continuously on the initial data. Our stability estimates are based
on the dispersion estimates due to time-asymptotic linear Vlasov
dynamics.