Invariance properties of the solution operator for measure-valued semilinear transport equations

Abstract

We provide conditions under which we prove for measure-valued transport equations

with non-linear reaction term in the space of finite signed Radon measures, that positivity

is preserved, as well as absolute continuity with respect to Lebesgue measure, if

the initial condition has that property.Moreover, if the initial condition has Lp regular density, then the solution has the same property.