Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities. Evers, J., Hille, S., & Muntean, A. SIAM Journal on Mathematical Analysis, 2016. doi abstract bibtex © by SIAM. In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and ux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 1068-1097] 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.
@article{
title = {Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities},
type = {article},
year = {2016},
keywords = {Measure-valued equations,Mild solutions,Nonlinearities,Particle systems,Time discretization,Ux boundary con-dition},
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abstract = {© by SIAM. In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and ux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 1068-1097] 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.},
bibtype = {article},
author = {Evers, J.H.M. and Hille, S.C. and Muntean, A.},
doi = {10.1137/15M1031655},
journal = {SIAM Journal on Mathematical Analysis},
number = {3}
}
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