Well-posedness of the ADMB-KdV equation in Sobolev spaces of negative indices

DOI10.1007/s40306-014-0050-7zbMath1300.35122OpenAlexW2095071003MaRDI QIDQ744444

Reza Pourgholi, Amin Esfahani

Publication date: 25 September 2014

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40306-014-0050-7

zbMATH Keywords

Sobolev spacesCauchy problemanisotropic dissipation-modified Boussinesq-Korteweg-de Vries (ADMB-KdV) equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Function spaces arising in harmonic analysis (42B35) PDEs of mixed type (35M10) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items (1)

Lipschitz stability of an inverse source problem for ADMB-KdV equation

Cites Work

• Unnamed Item
• The Cauchy problem for the dissipation-modified Kadomtsev-Petviashvili equation
• Dissipative solitons. From optics to biology and medicine
• Resonant decompositions and the \(I\)-method for the cubic nonlinear Schrödinger equation on \(\mathbb R^2\)
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• Stability of periodic waves generated by long-wavelength instabilities in isotropic and anisotropic systems
• Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
• Multilinear estimates for periodic KdV equations, and applications
• An evaluation of a model equation for water waves
• The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments
• The Cauchy problem for dissipative Korteweg de Vries equations in Sobolev spaces of negative order
• Cauchy problem for a model of nonlinear waves generated in viscous films
• The Global Cauchy Problem in Bourgain's-Type Spaces for a Dispersive Dissipative Semilinear Equation
• A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
• A bilinear estimate with applications to the KdV equation
• Nonuniqueness and Uniqueness in the Initial-Value Problem for Burgers’ Equation
• Quadratic forms for the 1-D semilinear Schrödinger equation

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