Estimates for a class of oscillatory integrals and decay rates for wave-type equations()

This paper investigates higher order wave-type equations of the form [Formula: see text] , where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. Using methods from harmonic analysis, we first establish global point...

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Detalles Bibliográficos
Autores principales: Arnold, Anton, Kim, JinMyong, Yao, Xiaohua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Academic Press 2012
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3617813/
https://www.ncbi.nlm.nih.gov/pubmed/23576817
http://dx.doi.org/10.1016/j.jmaa.2012.04.070
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author Arnold, Anton
Kim, JinMyong
Yao, Xiaohua
author_facet Arnold, Anton
Kim, JinMyong
Yao, Xiaohua
author_sort Arnold, Anton
collection PubMed
description This paper investigates higher order wave-type equations of the form [Formula: see text] , where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. Using methods from harmonic analysis, we first establish global pointwise time–space estimates for a class of oscillatory integrals that appear as the fundamental solutions to the Cauchy problem of such wave equations. These estimates are then used to establish (pointwise-in-time) [Formula: see text] estimates on the wave solution in terms of the initial conditions.
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spelling pubmed-36178132013-04-08 Estimates for a class of oscillatory integrals and decay rates for wave-type equations() Arnold, Anton Kim, JinMyong Yao, Xiaohua J Math Anal Appl Article This paper investigates higher order wave-type equations of the form [Formula: see text] , where the symbol [Formula: see text] is a real, non-degenerate elliptic polynomial of the order [Formula: see text] on [Formula: see text]. Using methods from harmonic analysis, we first establish global pointwise time–space estimates for a class of oscillatory integrals that appear as the fundamental solutions to the Cauchy problem of such wave equations. These estimates are then used to establish (pointwise-in-time) [Formula: see text] estimates on the wave solution in terms of the initial conditions. Academic Press 2012-10-01 /pmc/articles/PMC3617813/ /pubmed/23576817 http://dx.doi.org/10.1016/j.jmaa.2012.04.070 Text en © 2012 Elsevier Inc. https://creativecommons.org/licenses/by-nc-nd/3.0/ Open Access under CC BY-NC-ND 3.0 (https://creativecommons.org/licenses/by-nc-nd/3.0/) license
spellingShingle Article
Arnold, Anton
Kim, JinMyong
Yao, Xiaohua
Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title_full Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title_fullStr Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title_full_unstemmed Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title_short Estimates for a class of oscillatory integrals and decay rates for wave-type equations()
title_sort estimates for a class of oscillatory integrals and decay rates for wave-type equations()
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3617813/
https://www.ncbi.nlm.nih.gov/pubmed/23576817
http://dx.doi.org/10.1016/j.jmaa.2012.04.070
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AT yaoxiaohua estimatesforaclassofoscillatoryintegralsanddecayratesforwavetypeequations

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