Charla 152: Weak Asymptotic Analysis for scalar conservation laws with nonlocal flux- Analytical aspects, and numerical approximation

Conferencista: Juan Carlos Juajibioy. Profesor Escuela de Matemáticas, UPTC

Fecha: Miércoles 17 de Abril de 2024, 3:00 p.m.

Lugar: C-119

Resumen: In recent years, scalar conservation laws with nonlocal flux have been studied, considering the numerical results obtained in the works of P. Amorin (SIAM M2AN, 2015) and S. Blandin, P. Goatin (Numer. Math (2015). These class of first order nonliner equations offer a wide range of physical applications, and, since the standard theory known from local conservation laws often fails in this setting, there is a strong need to develop new mathematical tools and methods the nonlocal behavior.
In this context, we analyze numerical aspects using the Lagrangian-Eulerian approach. This method, developed by the research group of Professor Eduardo Abreu from IMECC-UNICAMP, results suitable to analyze the behavior of nonlocal scalar conservation laws. Moreover, these numerical results are formalized in the framework of the weak asymptotic method developed by E. Abreu, M. Panov, and E. Panov (JMAA 2016).