Control of the Continuity Equation with a Non Local Flow

By Rinaldo M. Colombo, Michael Herty, M. Mercier. 2009

147 citations recorded by the source corpus.

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differen- tiability of solutions with respect to the initial datum and characterize this derivative. A necessary condition for the optimality of suitable integral functionals then follows.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/d5bd580887e0c9eb02948ee1ebe85c73c6fa26c2

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Ocean Engineering

Citations in the corpus

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.”
Nonlocal Crowd Dynamics Models for Several Populations (2011, background): “4) in the case of one population, as soon as η ∈ C(2)c(R d;R+) and ‖η‖ L1 = 1, considered in [6].”
A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC (2011, methodology): “Using the techniques in [7, 9], we now obtain the continuous dependence of the solution to (1.”
On the Numerical Integration of Scalar Nonlocal Conservation Laws (2015, background): “which slightly extends, in the 1D case, the class of equations considered in [2, 7, 8].”
Analysis of a conservation law modeling a highly re-entrant manufacturing system (2009, background): “The organization of the following sections is as follows: First we rigorously prove the existence of weak solutions of the Cauchy problem for the conservation law (1) for the case when the initial data and boundary condition (2) lie in L1(0, 1) and L1(0, T ), respectively.”