Asymptotics for the Ostrovsky-Hunter equation in the critical case
type: Item
instance of: scholarly article
title: Asymptotics for the Ostrovsky-Hunter equation in the critical case
zbMATH Open document ID: 1487.35339
DOI: 10.1155/2017/3879017
author: Fernando Bernal-Vílchis
author: Nakao Hayashi
author: Pavel I. Naumkin
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: We consider the Cauchy problem for the Ostrovsky-Hunter equation \[\partial_x (\partial_t u - (b / 3) \partial_x^3 u - \partial_x \mathcal{K} u^3) = a u, \quad (t, x) \in \mathbb{R}^2, \quad u (0, x) = u_0(x), \ x \in \mathbb{R}, \] where \(a b > 0\). Define \(\xi_0 = (27 a / b)^{1 / 4}\). Suppose that \(\mathcal{K}\) is a pseudodifferential operator with a symbol \(\widehat{K} (\xi)\) such that \(\widehat{K} (\pm \xi_0) = 0\), \(\Im\widehat{K}(\xi) = 0\), and \(|\widehat{K} (\xi)| \leq C\). For example, we can take \(\widehat{K} (\xi) = (\xi^2 - \xi_0^2 )/ (\xi^2 + 1)\). We prove the global in time existence and the large time asymptotic behavior of solutions.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 6915934
Wikidata QID: Q59144286
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3879017
OpenAlex ID: W2580366307
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description: scientific article; zbMATH DE number 6915934