Global weak solutions for a generalized Dullin-Gottwald-Holm equation in the space \(H^1(\mathbb R)\)

DOI10.1186/s13661-014-0203-6zbMath1304.35557OpenAlexW2044437982WikidataQ59323222 ScholiaQ59323222MaRDI QIDQ481481

Shaoyong Lai, Meng Wu

Publication date: 12 December 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-014-0203-6

zbMATH Keywords

global weak solutionDullin-Gottwald-Holm equationviscous approximation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

Cites Work

• Unnamed Item
• Global existence of weak solutions for a shallow water equation
• Existence and uniqueness of low regularity solutions for the Dullin-Gottwald-Holm equation
• Global conservative solutions of the Camassa-Holm equation
• The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation
• Blow-up of solutions to the DGH equation
• Blow up and propagation speed of solutions to the DGH equation
• Compact sets in the space \(L^ p(0,T;B)\)
• Wave breaking for nonlinear nonlocal shallow water equations
• A note on well-posedness for Camassa-Holm equation.
• Global weak solutions for a shallow water equation
• A few remarks on the Camassa-Holm equation.
• Extension on peaked wave solutions of CH-\(\gamma\) equation
• The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in \(H^1(\mathbb R)\)
• Global conservative solutions of the Dullin-Gottwald-Holm equation
• Wellposedness for a parabolic-elliptic system
• On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
• Global weak solutions for the Dullin-Gottwald-Holm equation
• On the weak solutions to a shallow water equation
• Global weak solutions for a shallow water equation
• A Modern Introduction to the Mathematical Theory of Water Waves
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation

This page was built for publication: Global weak solutions for a generalized Dullin-Gottwald-Holm equation in the space \(H^1(\mathbb R)\)