On the Gevrey wellposedness of the Cauchy problem for weakly hyperbolic equations of 4th order
type: Item
instance of: scholarly article
title: On the Gevrey wellposedness of the Cauchy problem for weakly hyperbolic equations of 4th order
zbMATH Open document ID: 1123.35314
author: Ferruccio Colombini
author: Tamotu Kinoshita
published in: Hokkaido Mathematical Journal
publication date: 2002-06-06T00:00:00Z
review text: The authors consider the Cauchy problem for the fourth-order partial differential equation \(D^4_t-\sum_{|\alpha|=2}b_\alpha(t)D^\alpha_xD^2_tu+ \sum_{|\alpha|=4}c_\alpha(x)D^\alpha_xu=0\), \(D^h_tu(0,x)=u_h(x)\), \(h=0,1,2,3\). The equation is assumed to be weakly hyperbolic with coefficients in the Hölder class \(C^r\), \(0<r\leq 1\). Under suitable assumptions, allowing multiplicity 4 of the roots, the authors obtain the global well-posedness for data in the Gevrey class \(G^s\), \(1\leq s<1+(r/4)\). Under different hypotheses, which imply that the multiplicity is at most 2, well-posedness is proved for \(1\leq s<1+(r/2)\).
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35L30
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 1751371
reviewed by: Luigi Rodino
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911769
OpenAlex ID: W2024601519
DOI: 10.14492/HOKMJ/1350911769
description: scientific article; zbMATH DE number 1751371