Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610054 | Journal of Differential Equations | 2015 | 30 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Joep H.M. Evers, Sander C. Hille, Adrian Muntean,