Zero Diffusion-dispersion-smoothing Limits for Scalar Conservation Law with Discontinuous Flux Function

Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function

Zero Diffusion-Dispersion Limits for Scalar Conservation Laws

We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous solutions of the hyperbolic conservation law. The proof relies on the method of compensated compactness in the L 2 setting. Our result improves upon Schonbek's earl...

On the Compactness for Two Dimensional Scalar Conservation Law with Discontinuous Flux

We prove that a family of solutions to a Cauchy problem for a two dimensional scalar conservation law with a discontinuous smoothed flux and the vanishing viscosity is strongly Lloc– precompact under a new genuine nonlinearity condition, weaker than in previous works on the subject.

Existence and Uniqueness for Multidimensional Scalar Conservation Law with Discontinuous Flux

We prove existence and uniqueness of an entropy solution to a multidimensional scalar conservation law with discontinuous flux. The proof is based on the corresponding kinetic formulation of the considered equation and a ”smart” change of an unknown function.

Optimal Results On TV Bounds For Scalar Conservation Laws With Discontinuous Flux

This paper is concerned with the total variation of the solution of scalar conservation law with discontinuous flux in one space dimension. One of the main unsettled questions concerning conservation law with discontinuous flux was the boundedness of the total variation of the solution near interface. In [1], it has been shown by a counter example at T = 1, that the total variation of the solut...