ISAAC-ICMAM Conference of Analysis in Developing Countries 2024.
https://www.matua.edu.co/isaac-icmam-conference-of-analysis-in-developing-countries-2024/
The ISAAC-ICMAM (Virtual) Conference of Analysis in Developing Countries represents a significant collaboration between ISAAC and ICMAM Latin America. This jointly organized conference aims to share mathematical research in Latin America and the Caribbean, enhance its visibility, and foster collaboration among mathematicians from the region and worldwide.
During the conference, the following speak will be presented by Eduardo Abreu (Universidade Estadual de Campinas, UNICAMP, Brazil):
Title: A forward-tracking Lagrangian-Eulerian method for multidimensional systems of conservation laws
Abstract: We will discuss a forward Lagrangian-Eulerian approach to undertake a numerical-analytical study of inherent properties of multidimensional nonlinear hyperbolic conservation laws [(2024) https://doi.org/10.1016/j.cam.2023.115465]. It is widely known that their solutions can exhibit very complex behavior including the simultaneous presence of smooth waves, wave breaking, and shock waves. The novel forward tracking Lagragian-Eulerian formulation is based on the improved concept of no-flow curves. In the context of multidimensional hyperbolic systems of conservation laws, the resulting Lagrangian-Eulerian method satisfies a weak positivity principle in view of results of P. Lax and X.-D. Liu [Computational Fluid Dynamics Journal, 5(2) (1996) 133-156 and [Journal of Computational Physics, 187 (2003) 428-440]. We also found in [(2023) https://doi.org/10.1007/s10884-023-10283-1] a connection between the notion of no-flow curves, viewed as a vector field with locally bounded variation, and the results of A. Bressan in the context of existence and continuous dependence for discontinuous O.D.E.’s [Proc. Amer. Math. Soc. 104 (1988), 772-778]. We have tested the approach for well-known non-trivial muitlt-D systems and complex problems in fluid dynamics [(2023) https://doi.org/10.1016/j.amc.2022.127776, (2023) https://link.springer.com/article/10.1007/s10915-021-01712-8 , (2021) https://doi.org/10.1007/s10915-020-01392-w]: 4 by 4 compressible Euler equations (Double Mach Reflection problem and Mach 3 wind tunnel flow, the 3 by 3 shallow-water system with and without bottom topography, and the 8 by 8 Orszag-Tang vortex system in magnetohydrodynamics and a nonclassical 2 by 2 three-phase flow system of non strictly hyperbolic conservation laws with a resonance/umbilic point.