Blow-up of solution of an initial boundary value problem for a generalized Camassa-Holm equation

TL;DR

This paper investigates the conditions under which solutions to a generalized Camassa-Holm equation blow up, establishing local well-posedness and deriving a blow-up criterion using multiplier techniques.

Contribution

It introduces a new analysis of blow-up phenomena for a generalized Camassa-Holm equation, including well-posedness and conservation law derivation.

Findings

Established local well-posedness using Kato theorem

Derived a conservation law via multiplier technique

Presented a blow-up result for solutions

Abstract

In this paper, we study an initial boundary value problem for a generalized Camassa-Holm equation. We establish local well-posedness of this closed-loop system by using Kato theorem for abstract quasilinear evolution equation of hyperbolic type. Then, by using multiplier technique, we obtain a conservation law which enable us to present a blow-up result.