Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow

By Gianluca Crippa, Magali L'ecureux-Mercier. 2011

106 citations recorded by the source corpus.

In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local flow. We also give a stability result with respect to various parameters.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3e2ee679152280996cf323968ff72824aa76a712

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

On the Numerical Integration of Scalar Nonlocal Conservation Laws (2015, background): “Remark that in the nonlocal case, well posedness results are available also in the case of systems in several space dimensions, see [8,10].”
Nonlocal Crowd Dynamics Models for Several Populations (2011, background): “5) are considered also in [8], where measure theoretic techniques are exploited.”
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “For the underlying dynamics existence and uniqueness [35, 40, 45, 44, 46, 12, 25], (optimal) control problems [33, 4, 14, 19, 38, 24], and suitable numerical schemes [1, 11, 13, 28, 52] have been analyzed.”