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Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
Eindhoven University of Technology, Netherlands.
Leiden University, Netherlands.
Eindhoven University of Technology, Netherlands. (Mathematics)ORCID iD: 0000-0002-1160-0007
2015 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 3, p. 1068-1097Article in journal (Refereed) Published
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Abstract [en]

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space 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.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 259, no 3, p. 1068-1097
Keywords [en]
Measure-valued equations, flux boundary condition, mild solutions, boundary layer asymptotics, singular limit, convergence rate
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-39773DOI: 10.1016/j.jde.2015.02.037ISI: 000354665900010Scopus ID: 2-s2.0-84928759422OAI: oai:DiVA.org:kau-39773DiVA, id: diva2:901184
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cited By 1

Available from: 2016-02-06 Created: 2016-02-06 Last updated: 2017-05-30Bibliographically approved

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Muntean, Adrian

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