4 papers
Failure of uniqueness for scalar conservation laws
Shyam Sundar Ghoshal, Abraham Sylla, Parasuram Venkatesh
In this article, we develop the first negative results for scalar conservation laws with finite speed of propagation. While the work of Gargyants, Goritsky, and Panov establishes n…
Front Tracking for Scalar Conservation Laws with Spatially Heterogeneous Flux
Parasuram Venkatesh
In this article, we propose a novel front tracking scheme for scalar conservation laws with spatially heterogeneous, uniformly convex flux and prove that approximations converge to…
Stability of Simple Shocks for Spatially Heterogeneous Conservation Laws
Shyam Sundar Ghoshal, Parasuram Venkatesh
In this paper, we consider scalar conservation laws with smoothly varying spatially heterogeneous flux that is convex in the conserved variable. We identify structural assumptions…
A Non-Conservative, Non-Local Approximation of the Burgers Equation
Shyam Sundar Ghoshal, Parasuram Venkatesh, Emil Wiedemann
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena…