Ill-posedness for the \(b\)-family of equations
From MaRDI portal
Publication:347064
DOI10.1007/s00332-016-9302-0zbMath1356.37079OpenAlexW2474802329MaRDI QIDQ347064
A. Alexandrou Himonas, Katelyn Grayshan, Curtis Holliman
Publication date: 30 November 2016
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00332-016-9302-0
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear ill-posed problems (47J06) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)
Related Items
The power series method for nonlocal and nonlinear evolution equations, Instability and nonuniqueness for the \(b\)-Novikov equation, Radius of analyticity for the Camassa-Holm equation on the line, The stability of the b-family of peakon equations, Construction of 2-Peakon Solutions and Ill-Posedness for the Novikov Equation, Ill-posedness for the Camassa-Holm and related equations in Besov spaces, Spectral Instability of Peakons in the $b$-Family of the Camassa--Holm Equations, Ill-posedness of the Cauchy problem for the \(\mu\)-Camassa-Holm-type equations, Well-posedness and continuity properties of the Degasperis-Procesi equation in critical Besov space, On well-posedness of nonlocal evolution equations, Construction of peakon-antipeakon solutions and ill-posedness for the b-family of equations, Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity, Large time behavior for the support of momentum density of the Holm-Staley \(b\)-family equation with weakly dissipative term, Non-uniqueness for the Fokas-Olver-Rosenau-Qiao equation, Construction of 2-peakon solutions and nonuniqueness for a generalized mCH equation, Growth of Perturbations to the Peaked Periodic Waves in the Camassa--Holm Equation, Stability of smooth solitary waves in the \(b\)-Camassa-Holm equation, 2-peakon solutions and non-uniqueness of the Fokas-Olver-Rosenau-Qiao equation with higher-order nonlinearity, Existence, persistence, and continuation of solutions for a generalized 0-Holm-Staley equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Euler equations on a semi-direct product of the diffeomorphisms group by itself
- Continuity properties of the data-to-solution map for the periodic \(b\)-family equation.
- Non-uniform dependence on initial data for the CH equation on the line.
- Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models
- On well-posedness of the Degasperis-Procesi equation
- On the well-posedness of the Degasperis-Procesi equation
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- On the Cauchy problem for the periodic \(b\)-family of equations and of the non-uniform continuity of Degasperis-Procesi equation
- Global weak solutions and blow-up structure for the Degasperis-Procesi equation
- Global conservative solutions of the Camassa-Holm equation
- Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Ill-posedness of the Navier-Stokes equations in a critical space in 3D
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Breakdown of a shallow water equation
- Multipeakons and the classical moment problem
- Closed-loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances
- Traveling wave solutions of the Degasperis-Procesi equation
- On the ill-posedness of some canonical dispersive equations.
- Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE
- Stability of the Camassa-Holm solitons
- Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
- Non-uniform continuity in \(H^1\) of the solution map of the CH equation
- Global existence and blow-up phenomena for the Degasperis-Procesi equation
- Persistence properties and unique continuation of solutions of the Camassa-Holm equation
- Numerical study of traveling-wave solutions for the Camassa--Holm equation
- Traveling wave solutions of the Camassa-Holm equation
- Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation
- Global solutions and blow-up phenomena for the periodic b -equation
- On solutions to the Holm–Staleyb-family of equations
- Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
- A Note on the Local Well-Posedness for the Whitham Equation
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Non-Uniform Dependence for the Periodic CH Equation
- A numerical and theoretical study of certain nonlinear wave phenomena
- A shallow water equation on the circle
- Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
- Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- Breakdown of the Camassa-Holm equation
- Perturbative symmetry approach
- Multi-peakon solutions of the Degasperis–Procesi equation
- An integrable shallow water equation with peaked solitons
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- A bilinear estimate with applications to the KdV equation
- A Class of Equations with Peakon and Pulson Solutions (with an Appendix by Harry Braden and John Byatt-Smith)
- Existence time for the Camassa-Holm equation and the critical Sobolev index
- Variational methods and applications to water waves
- The Cauchy problem for a generalized Camassa-Holm equation