The generalized BBM-Burgers equations: convergence results for conservation law with discontinuous flux function

Abstract

We consider conservation laws with discontinuous flux, which are regularized with generalized BBM-Burgers equations. We study the convergence of one sequence of solutions of these equations for one solution of the associated conservation law. In the multidimensional case, we prove one convergence result using the H-measures and in the one-dimensional case, we use the method of compensated compactness.

Keywords:

• convergence of solutions
• partial differential equations
• H-measures
• compensated compactness
• discontinuous flux function

AMS Subject Classifications:

• Primary: 35L65
• Secondary: 76N10

Additional information

Funding

The second author was supported by Capes, Grant. 10053/12-3, Brazil.