Talk by Rahul Barthwal
Posted on: 25 Aug 2026
Title: Existence of global solutions for some hyperbolic systems via novel regularizations
Speaker: Rahul Barthwal, Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany
Date: 2 September 2026
Time: 2 PM IST
Venue: TIFRCAM Auditorium and Zoom
Abstract: We discuss the global existence of weak (entropy) solutions for two distinct classes of hyperbolic systems by constructing novel viscous regularizations. In the first part of the talk,, we focus on a class of 2 × 2 Keyfitz-Kranzer systems arising in thin film flows. Because the standard diagonal viscous approximation fails to yield the appropriate mathematical structure, we instead construct a novel viscous regularization inspired by lubrication equations. This approach provides the critical compactness estimates necessary to establish the existence of weak entropy solutions via the vanishing diffusion limit [1].
In the second part of the talk, we generalize these results to n×n systems of a broader KeyfitzKranzer class covering several important physical models. We introduce a new artificial viscous regularization aligned with the nonlinear field, which yields a parabolic equation for the Riemann invariant associated with the nonlinear field, coupled with transport equations for the remaining Riemann invariants. This structure drives the compactness argument and yields global existence of weak solutions for the inviscid system [2].
(Based on the joint works with Christian Rohde (University of Stuttgart), Phillipp Öffner (TU Clausthal) and Lilu Sahu(IIT Kharagpur))
References
- R. Barthwal, P. Öffner, and C. Rohde. Global Existence for a Class of Keyfitz–Kranzer Systems. Accepted for publication at Journal of Hyperbolic Differential Equations, 2026.
- R. Barthwal and L. Sahu. Weak solutions for a class of n × n hyperbolic systems and shock stability for the viscous approximation. In preparation, 2026.