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

Hille, S.C.; Lyons, R.; Muntean, A. (2025)

Article / Letter to editor

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 L^p regular
density, then the solution has the same property.

• Measure-valued transport equations
• Mild solutions
• Measure-valued solutions
• Invariance properties

• All authors: Hille, S.C.; Lyons, R.; Muntean, A.
• Date: 2025-06-22
• Journal: Analysis and Mathematatical Physics
• Volume: 15
• DOI: doi:10.1007/s13324-025-01093-3
• Link: https://link.springer.com/article/10.1007/s13324-025-01093-3#citeas