In this paper, we consider the convergence problem of Kawahara equationut+α∂x5u+β∂x3u+∂x(u2)=0 on real line with rough data. Firstly, by using Strichartz estimates as well high-low frequency idea, establish two crucial bilinear estimates, which are just Lemma 3.1, 3.2 in paper; also present proof 3.3 shows that s>−12 is necessary for 3.2. Secondly, truncated technique and technique, show pointw...

In this paper, we consider initial-boundary value problem on a semiaxis for the generalized Kawahara equation with higher-order nonlinearity. We obtain result existence and uniqueness of global solution. Also, if contains an absorbing term vanishing at infinity, prove that solution decays large time values.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 21 January 2021Accepted: 20 June 2021Published online: 09 September 2021KeywordsKawahara equation, spectral stability, high-frequency instabilities, perturbation methods, dispersive Hamiltonian systems, Stokes wavesAMS Subject Headings35B35, 37K45, 34L05Publication DataIS...

We consider the Kawahara equation, a fifth order Korteweg-de Vries type posed on bounded interval. The first result of article is related to well-posedness in weighted Sobolev spaces, which one was shown using general version Lax--Milgram Theorem. With respect control problems, we will prove two results. First, if region neighborhood right endpoint, an exact controllability spaces established. ...

Abstract In this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative approximation scheme presented to solve initial boundary value problem of equation, which preserves original properties. The proposed based on finite difference method. existence solutions has been shown by Browder fixed point theorem. priori bound and error estimates, as well cons...