A singular limit problem for the Ibragimov-Shabat equation
A singular limit problem for the Ibragimov-Shabat equation
We consider the Ibragimov-Shabat equation, which contains nonlinear dispersive effects. We provethat as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the …