Non-uniform dependence and well-posedness for the hyperelastic rod equation
type: Item
instance of: scholarly article
title: Non-uniform dependence and well-posedness for the hyperelastic rod equation
zbMATH Open document ID: 1193.35221
author: David Karapetyan
published in: Journal of Differential Equations
publication date: 2010-07-22T00:00:00Z
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 5759042
zbMATH Keywords: hyperelastic rod equation
zbMATH Keywords: periodic
zbMATH Keywords: non-periodic
zbMATH Keywords: initial value problem
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: well-posedness
zbMATH Keywords: continuity of solution map
zbMATH Keywords: non-uniform dependence
zbMATH Keywords: approximate solutions
zbMATH Keywords: energy estimates
MaRDI profile type: Publication
full work available at URL: j.jde.2010.04.002
OpenAlex ID: W1996844149
cites work: \(H^1\)-Perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation
cites work: Model equations for long waves in nonlinear dispersive systems
cites work: Sharp well-posedness results for the BBM equation
cites work: Global conservative solutions of the Camassa-Holm equation
cites work: Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
cites work: Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
cites work: Stability of a class of solitary waves in compressible elastic rods
cites work: Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
cites work: Head-on collision between two solitary waves in a compressible Mooney-Rivlin elastic rod.
cites work: Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
cites work: Q5565769
cites work: Q4255465
cites work: Non-uniform dependence on initial data for the CH equation on the line.
cites work: Non-Uniform Dependence for the Periodic CH Equation
cites work: The Cauchy problem for an integrable shallow-water equation
cites work: Q3367828
cites work: Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics
cites work: Non-uniform continuity in \(H^1\) of the solution map of the CH equation
cites work: Global conservative solutions of the generalized hyperelastic-rod wave equation
cites work: Q4075341
cites work: Commutator estimates and the euler and navier-stokes equations
cites work: On the ill-posedness of some canonical dispersive equations.
cites work: Q5714604
cites work: Traveling waves in compressible elastic rods
cites work: Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
cites work: Global Conservative Solutions of the Hyperelastic Rod Equation
cites work: Non-uniform dependence on initial data for a family of non-linear evolution equations.
cites work: On the Cauchy problem for the Camassa-Holm equation
cites work: Pseudodifferential operators and nonlinear PDE
cites work: On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation
cites work: Local well‐posedness and blow‐up criteria of solutions for a rod equation
DOI: 10.1016/J.JDE.2010.04.002
Recommended article: On the well-posedness of the hyperelastic rod equation
Recommended article: Existence of solutions for a finite nonlinearly hyperelastic rod
Recommended article: Blow-up issues for the hyperelastic rod equation
Recommended article: On an initial-boundary value problem for the hyperelastic rod wave equation
Recommended article: The Cauchy problem for the generalized hyperelastic rod wave equation
Recommended article: Q3571276
Recommended article: On solitonic solutions for the hyperelastic rod equation
Recommended article: Q3329818
Recommended article: Q3017096
Recommended article: Global Conservative Solutions of the Hyperelastic Rod Equation
description: scientific article; zbMATH DE number 5759042