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Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities
Simon Fraser University, Canada; Dalhousie University, Canada; Eindhoven University of Technology, Netherlands.
Leiden University, Netherlands.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). (Mathematics)ORCID iD: 0000-0002-1160-0007
2016 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 3, p. 1929-1953Article in journal (Refereed) Published
Abstract [en]

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Place, publisher, year, edition, pages
SIAM Publications , 2016. Vol. 48, no 3, p. 1929-1953
Keywords [en]
measure-valued equations; nonlinearities; time discretization; flux boundary condition; mild solutions; particle systems
National Category
Mathematics
Research subject
Mathematics; Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-41710DOI: 10.1137/15M1031655ISI: 000385019900012OAI: oai:DiVA.org:kau-41710DiVA, id: diva2:920073
Available from: 2016-04-15 Created: 2016-04-15 Last updated: 2018-12-19Bibliographically approved

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