The existence of the global entropy weak solutions for a generalized Camassa-Holm equation

TL;DR

This paper proves the existence of global entropy weak solutions for a generalized Camassa-Holm equation using viscous approximation, contributing to the mathematical understanding of such nonlinear PDEs.

Contribution

It establishes the existence of global entropy weak solutions for a generalized Camassa-Holm equation via viscous approximation methods.

Findings

Existence of global entropy weak solutions in H^1(R)

Solutions have derivatives in L^1(R) and BV(R)

Method uses viscous approximation

Abstract

In this paper, we prove the existence of a global entropy weak solution $u\in H^1(\mathbb{R})$ and $\partial_{x}u\in L^1(\mathbb{R})\cap BV(\mathbb{R})$ for the Cauchy problem of a generalized Camassa-Holm equation by the viscous approximation method.