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of small-amplitude Boltzmann shocks
Gevrey regularizing effect of the Cauchy problem for non-cutoff
homogeneous Kac's equation
In this work, we consider a spatially homogeneous Kac's equation
with a non cutoff cross section. We prove that the weak solution of
the Cauchy problem is in the Gevrey class for positive time. This
is a Gevrey regularizing effect for non smooth initial datum. The
proof relies on the Fourier analysis of Kac's operators and on an
exponential type mollifier.