Heterogeneous Conservation Laws: Well-Posedness, Approximation and Application
Abraham Sylla, Université de Picardie Jules Verne, France
| Speaker |
Abraham Sylla, Université de Picardie Jules Verne, France
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|---|---|
| When |
Jul 15, 2025
from 04:00 PM to 05:00 PM |
| Where | LH-111, First Floor |
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COLLOQUIUM TALK
Title: Heterogeneous Conservation Laws: Well-Posedness, Approximation and Application
Abstract: We present results regarding 1D scalar conservation law with spatial heterogeneity.
Firstly, we discuss the well-posedness. A particuliar focus is given to the approximation by a finite volume scheme using the theory of discontinuous flux. Then, we present an extension of the results obtained by Colombo and Perrollaz about the Inverse Design problem. The key ingredients are the notion of generalized characteristics of Dafermos and the correspondence with the associated Hamilton-Jacobi equation. Numerical simulations are presented to highlight the differences with the homogeneous case.
Joint works with Rinaldo Colombo (University of Brescia, Italy) and Vincent Perrollaz (Unversity of Tours, France)
Speaker Bio: Abraham Sylla is a faculty member at the Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), Université de Picardie Jules Verne, France. His research interests include entropy solutions of conservation laws, finite volume schemes, macroscopic traffic flow models, and viscosity solutions of Hamilton-Jacobi equations.