Local well-posedness for Kawahara equation

zbMath1298.35176MaRDI QIDQ633877

Takamori Kato

Publication date: 30 March 2011

Published in: Advances in Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Norm inflation for the generalized Boussinesq and Kawahara equations ⋮ Kawahara-Burgers equation on a strip ⋮ Convergence problem of the Kawahara equation on the real line ⋮ Global well-posedness for the fifth-order mKdV equation ⋮ The dynamic properties of a generalized Kawahara equation with Kuramoto-Sivashinsky perturbation ⋮ Properties of the support of solutions of a class of nonlinear evolution equations ⋮ Control and stabilization of the periodic fifth order Korteweg-de Vries equation ⋮ Control of Kawahara equation with overdetermination condition: The unbounded cases ⋮ On solitary-wave solutions of fifth-order KdV type of model equations for water waves ⋮ Low regularity for the Kawahara equation on the half‐line ⋮ Dispersive limit from the Kawahara to the KdV equation ⋮ Decay properties for solutions of fifth order nonlinear dispersive equations ⋮ Local controllability and stability of the periodic fifth-order KdV equation with a nonlinear dispersive term ⋮ Non-homogeneous initial-boundary-value problem of the fifth-order Korteweg-de Vries equation with a nonlinear dispersive term ⋮ The initial-boundary value problem for the Kawahara equation on the half-line ⋮ Well-posedness of the classical solutions for a Kawahara-Korteweg-de Vries-type equation ⋮ The Cauchy problem for higher-order modified Camassa-Holm equations on the circle ⋮ Unconditional well-posedness for the Kawahara equation ⋮ A Korteweg-de Vries type of fifth-order equations on a finite domain with point dissipation ⋮ Well-posedness issues on the periodic modified Kawahara equation ⋮ On the solutions for a Benney-Lin type equation ⋮ On the Cauchy problem for the strong dissipative fifth-order KdV equations ⋮ Initial-boundary value problem of fifth-order Korteweg-de Vries equation posed on half line with nonlinear boundary values ⋮ Global H4 solution for the fifth-order Kudryashov–Sinelshchikov–Olver equation

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