Time decay of solutions for generalized Boussinesq equations in two space dimensions
type: Item
instance of: scholarly article
title: Time decay of solutions for generalized Boussinesq equations in two space dimensions
zbMATH Open document ID: 0934.35130
author: Akmel Dé Godefroy
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-05T00:00:00Z
review text: The Cauchy problem for the two-dimensional generalized Boussinesq equations is considered. Local existence theorems are proved in two Sobolev spaces, with one of them being weighted. Through the Fourier transform, the system is reduced to integral equations and the contraction mapping argument is used. The study of decay in the supremum norm is first done for the linearized system. Then the same law of decay is established for the nonlinear system under the assumptions that initial data are small and \(p>6\) in the nonlinear term \(n^p n_{x}\).
reviewed by: V. V. Shelukhin
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1348142
zbMATH Keywords: local existence
zbMATH Keywords: time decay
zbMATH Keywords: Cauchy problem
zbMATH Keywords: generalized Boussinesq equations
zbMATH Keywords: Fourier transform
zbMATH Keywords: integral equations
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6470
OpenAlex ID: W2055660181
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DOI: 10.1006/JMAA.1999.6470
description: scientific article; zbMATH DE number 1348142