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Main Authors: Damanik, David, Li, Yong, Xu, Fei
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2201.02920
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author Damanik, David
Li, Yong
Xu, Fei
author_facet Damanik, David
Li, Yong
Xu, Fei
contents This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data.
format Preprint
id arxiv_https___arxiv_org_abs_2201_02920
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line
Damanik, David
Li, Yong
Xu, Fei
Analysis of PDEs
Mathematical Physics
This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data.
title The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2201.02920