Abstract
In this Letter, we study the following initial boundary value problem for a generalized Camassa–Holm equation { u t − u x x t + 3 u u x − 2 u x u x x − u u x x x + k ( u − u x x ) x = 0 , t ⩾ 0 , x ∈ [ 0 , 1 ] , u ( 0 , t ) = u ( 1 , t ) = u x ( 0 , t ) = u x ( 1 , t ) = 0 , t ⩾ 0 , u ( 0 , x ) = u 0 ( x ) , x ∈ [ 0 , 1 ] , where k is a real constant. We establish local well-posedness of this closed-loop system by using Kato's 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Physics Letters A
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
