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arXiv · 1507.05730

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

Joep H. M. Evers·Sander C. Hille·Adrian Muntean
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Abstract

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 [Evers, Hille and Muntean. Journal of Differential Equations, 259:1068-1097, 2015] 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 the results of [Evers, Hille and Muntean. Journal of Differential Equations, 259:1068-1097, 2015] 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 [Evers. PhD thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there, are now resolved.

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Joep H. M. Evers, Sander C. Hille, Adrian Muntean. 2015-07-21. Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities. https://arxiv.org/abs/1507.05730

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