Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups

Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups

We generalize the dispersive estimates and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on H-type groups, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral of the full Laplacian. The dimension of the center on...

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Main Authors: Heping Liu, Manli Song
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/219375
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spelling doaj-4df229243b904697a9b303cc5123c9392020-11-24T23:40:00ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/219375219375Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type GroupsHeping Liu0Manli Song1School of Mathematical Sciences, Peking University, Beijing 100871, ChinaSchool of Mathematical Sciences, Peking University, Beijing 100871, ChinaWe generalize the dispersive estimates and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on H-type groups, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral of the full Laplacian. The dimension of the center on those groups is p and we assume that p>1. A key point consists in estimating the decay in time of the L∞ norm of the free solution. This requires a careful analysis due also to the nonhomogeneous nature of the full Laplacian.http://dx.doi.org/10.1155/2014/219375
collection DOAJ
language English
format Article
sources DOAJ
author Heping Liu
Manli Song
spellingShingle Heping Liu
Manli Song
Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
Abstract and Applied Analysis
author_facet Heping Liu
Manli Song
author_sort Heping Liu
title Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
title_short Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
title_full Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
title_fullStr Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
title_full_unstemmed Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups
title_sort strichartz inequalities for the wave equation with the full laplacian on h-type groups
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We generalize the dispersive estimates and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on H-type groups, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral of the full Laplacian. The dimension of the center on those groups is p and we assume that p>1. A key point consists in estimating the decay in time of the L∞ norm of the free solution. This requires a careful analysis due also to the nonhomogeneous nature of the full Laplacian.
url http://dx.doi.org/10.1155/2014/219375
work_keys_str_mv AT hepingliu strichartzinequalitiesforthewaveequationwiththefulllaplacianonhtypegroups
AT manlisong strichartzinequalitiesforthewaveequationwiththefulllaplacianonhtypegroups
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