Mild solutions to a measure-valued mass evolution problem with flux boundary conditions

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0,1][0,1] endowed with a linear discontinuous production term, formulated in the space M([0,1])M([0,1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem. Keywords: Measure-valued equations; Flux boundary condition; Mild solutions; Boundary layer asymptotics; Singular limit; Convergence rate