Dispersive and diffisive limts for Otrovsky-Hunter type equation

TL;DR

This paper investigates the asymptotic behavior of the Ostrovsky-Hunter type equation with short pulse effects as a key parameter approaches zero, using a priori estimates and compensated compactness in L^p spaces.

Contribution

It provides new analytical insights into the dispersive and diffusive limits of the Ostrovsky-Hunter equation as the parameter gamma tends to zero.

Findings

Established asymptotic limits for the equation as gamma approaches zero.

Developed a priori estimates for solutions in L^p spaces.

Applied compensated compactness method to prove convergence.

Abstract

We consider the Ostrovsky-Hunter type equation that includes the short pulse. We con- sider here the asymptotic behavior as gamma goes to 0. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p set- ting.