Weakly hyperbolic equations with time degeneracy in Sobolev spaces
type: Item
instance of: scholarly article
title: Weakly hyperbolic equations with time degeneracy in Sobolev spaces
zbMATH Open document ID: 0938.35109
DOI: 10.1155/S1085337597000377
published in: Abstract and Applied Analysis
publication date: 2000-06-27T00:00:00Z
full work available at URL: https://eudml.org/doc/48430
full work available at URL: issue-3-4.html
review text: In this paper the author proves existence and uniqueness theorems in Sobolev spaces of time local solutions to the Canchy problem for weakly hyperbolic second order equation as follows \[ u_{tt}- \lambda(t)^2\Delta u=f\bigl(t,x,u_t, \mu_i(t) \partial_{x_i} u\bigr). \] In this equation the regularity loss of derivatives solutions occurs as in the case of linear equations. Under some assumptions on the functions \(\lambda(t),\mu(t)\) and \(f(t,x,u, p,q)\) the author determines precisely the loss of Sobolev regularity of solutions of the above nonlinear Cauchy problem.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35L80
zbMATH DE Number: 1370653
zbMATH Keywords: loss of Sobolev regularity
author: Michael Reissig
reviewed by: Kunihiko Kajitani
MaRDI profile type: Publication
OpenAlex ID: W2025493357
description: scientific article; zbMATH DE number 1370653