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…
A convergence rate result for front tracking approximations of conservation laws with discontinuous flux
Shyam Sundar Ghoshal, John D Towers
We consider the initial value problem for a scalar conservation law in one space dimension with a single spatial flux discontinuity, the so-called two-flux problem. We prove that a…
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…