The Cauchy problem for the Rosenau equation

DOI10.1016/j.na.2008.10.085zbMath1171.35424OpenAlexW2048343747MaRDI QIDQ1021742

Shubin Wang, Gui Xiang Xu

Publication date: 9 June 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.10.085

zbMATH Keywords

nonexistenceCauchy problempotential well methodfinite-time blow-upRosenau equationexistence of global solutionstable set and unstable set

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30) Initial value problems for higher-order hyperbolic equations (35L30) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (14)

The initial-boundary value problem for the generalized double dispersion equation ⋮ Global existence, asymptotic behavior, and regularity of solutions for time–space fractional Rosenau equations ⋮ The Cauchy problem for a class of the multidimensional Boussinesq-type equation ⋮ On global solutions for the Cauchy problem of a Boussinesq-type equation ⋮ Decay and scattering of small solutions for Rosenau equations ⋮ Existence and nonexistence of solutions for a generalized Boussinesq equation ⋮ The initial-boundary value problems for a class of sixth order nonlinear wave equation ⋮ Global existence and asymptotic behavior of solution for Rosenau equation with Stokes damped term ⋮ Solitary wave formation from a generalized Rosenau equation ⋮ Global existence and nonexistence of the initial-boundary value problem for the dissipative Boussinesq equation ⋮ Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation ⋮ Unnamed Item ⋮ Convergence analysis of the Galerkin finite element method for the fourth-order Rosenau equation ⋮ On the classical solutions for a Rosenau–Korteweg-deVries–Kawahara type equation

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