The global conservative solutions for the generalized Camassa-Holm equation
type: Item
instance of: scholarly article
title: The global conservative solutions for the generalized Camassa-Holm equation
zbMATH Open document ID: 1439.35007
author: Li Yang
author: Shouming Zhou
author: Xinyu Tu
author: Chunlai Mu
published in: Electronic Research Archive
publication date: 2020-04-15T00:00:00Z
review text: This paper deals with the continuation of solutions for the generalized Camassa-Holm equation \[ u_t-u_{txx}+\frac{(m+2)(m+1)}{2}u^mu_x=\Big(\frac{m}{2}u^{m-1}(u_x)^2+u^mu_{xx}\Big)_x, \] where \(m\) is a positive integer. They transform the previous equation to a semi-linear system using a new set of variables. Then they get the existence of global conservative solutions to the original equation by establishing the existence and uniqueness of the global solutions to the semi-linear system.
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 7189492
zbMATH Keywords: uniqueness
zbMATH Keywords: generic regularity
reviewed by: Giuseppe Maria Coclite
MaRDI profile type: Publication
full work available at URL: era.2019009
OpenAlex ID: W2980183173
cites work: Global conservative solutions of the Camassa-Holm equation
cites work: GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
cites work: Uniqueness of conservative solutions to the Camassa-Holm equation via characteristics
cites work: Generic regularity of conservative solutions to a nonlinear wave equation
cites work: Q4311808
cites work: An integrable shallow water equation with peaked solitons
cites work: The Hamiltonian structure of the Camassa-Holm equation
cites work: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
cites work: Stability of the Camassa-Holm solitons
cites work: Stability of peakons
cites work: Q4225587
cites work: GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION
cites work: Symplectic structures, their Bäcklund transformations and hereditary symmetries
cites work: Q4046802
cites work: On measures of accretion and dissipation for solutions of the Camassa–Holm equation
cites work: Generic Regularity of Conservative Solutions to Camassa--Holm Type Equations
cites work: Local Well-Posedness and Orbital Stability of Solitary Wave Solutions for the Generalized Camassa–Holm Equation
cites work: Conservation laws of the Camassa–Holm equation
cites work: Well-posedness and analyticity for the Cauchy problem for the generalized Camassa-Holm equation
cites work: On the Cauchy problem for the generalized Camassa-Holm equation
cites work: Uniqueness of conservative solutions to the generalized Camassa-Holm equation via characteristics
cites work: Persistence properties for a generalized Camassa-Holm equation in weighted \(L^p\) spaces
cites work: Well-posedness, blow-up phenomena and global existence for the generalized \(b\)-equation with higher-order nonlinearities and weak dissipation
cites work: Global conservative and dissipative solutions of the generalized Camassa-Holm equation
cites work: Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing
DOI: 10.3934/ERA.2019009
description: scientific article; zbMATH DE number 7189492