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APRG Seminar

Title: Nonlocal conservation laws: modeling, theory, and numerics
Speaker: Ganesh Vaidya (Penn State University, University Park, USA)
Date: 03 February 2025
Time: 10 am
Venue: Microsoft Teams (online)

This talk explores scalar and coupled systems of nonlocal conservation laws (hyperbolic partial differential equations) and their applications in modeling real-world phenomena such as traffic flow and crowd dynamics. The nonlocal nature of these laws makes them particularly effective in capturing dynamics where each individual or unit in the system moves based on its perception of density and its variations within a given horizon or neighborhood. This makes them ideal for studying large-scale systems, such as urban traffic, opinion formation, or massive crowd gatherings.

These partial differential equations often lack closed-form solutions, making it necessary to develop numerical algorithms that converge to the entropy (physical) solution. To this end, we develop and present finite-volume schemes to approximate these governing PDEs. For practical purposes, along with convergence, one also needs to investigate how errors depend on the mesh parameters. Thus, the talk focuses on establishing the convergence and rate of convergence of finite-volume approximations to the entropy solution.

Numerical experiments will be presented to validate the theoretical findings, illustrate the convergence rates, and highlight the practical relevance of these models.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 Feb 2025