Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations
type: Item
instance of: scholarly article
title: Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations
zbMATH Open document ID: 1439.35093
author: Emil Novruzov
published in: Journal of Differential Equations
publication date: 2018-10-02T00:00:00Z
review text: This paper considers the Cauchy problem for \[ (1-\partial_x^2)(u_t+f(u)_x)+\partial_x[g(u)+\frac{1}{2} f''(u)u_x^2]=0, \] where $x\in\mathbb{R}$, the initial condition is in $H^s(\mathbb{R})$ with $s>3/2$, $f$ and $g$ are smooth, $f''\geq \gamma$ for some positive constant $\gamma$, and $g$ is bounded above or bounded below. The main result is an improvement of a local blow-up criterion given by \textit{L. Brandolese} and \textit{M. F. Cortez} [J. Differ. Equations 256, No. 12, 3981--3998 (2014; Zbl 1293.35053); J. Funct. Anal. 266, No. 12, 6954--6987 (2014; Zbl 1295.35009)], along similar lines.
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35G25
zbMATH DE Number: 6946028
zbMATH Keywords: rod equation
zbMATH Keywords: shallow water
MaRDI profile type: Publication
full work available at URL: j.jde.2017.06.031
OpenAlex ID: W2734999599
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DOI: 10.1016/J.JDE.2017.06.031
description: scientific article; zbMATH DE number 6946028