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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 19
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 4, August 2012
  4. Well-posedness and stability results for the Gardner equation
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 6, December 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 5, October 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 4, August 2012
Branches of forced oscillations for a class of constrained ODEs: a topological approach
Asymptotic expansion of radial solutions for supercritical biharmonic equations
Multiple variational solutions to nonlinear Steklov problems
Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence
Global existence and asymptotic behavior of solutions to the homogeneous Neumann problem for ILW equation on a half-line
Well-posedness of the Cauchy problem for nonlinear parabolic equations with variable density in the hyperbolic space
Well-posedness and stability results for the Gardner equation
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 3, June 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 2, April 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 1, February 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Well-posedness and stability results for the Gardner equation

Content Provider SpringerLink
Author Alejo, Miguel A.
Copyright Year 2011
Abstract In this article we present local well-posedness results in the classical Sobolev space $${H^{s}(\mathbb{R})}$$ with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space $${H^{1}(\mathbb{R})}$$ where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.
Ending Page 520
Page Count 18
Starting Page 503
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 19
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-10-12
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Local well posedness Stability KdV-like equations (Korteweg-de Vries) Integrability Analysis Soliton-like equations Sensitivity, stability, well-posedness Nonlinear evolution equations Gardner equation
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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