Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping

Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping

In this paper, we consider the asymptotic behavior of solutions to the p-system with time-dependent damping on the half-line R+=0,+∞, vt−ux=0,ut+pvx=−α/1+tλu with the Dirichlet boundary condition ux=0=0, in particular, including the constant and nonconstant coefficient damping. The initial data v0,u...

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Main Authors: Ran Duan, Mina Jiang, Yinghui Zhang
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/3060867
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spelling doaj-fcc419a37e0740188db082583c9dd4392021-07-02T06:54:28ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/30608673060867Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent DampingRan Duan0Mina Jiang1Yinghui Zhang2School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, ChinaSchool of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, ChinaSchool of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, ChinaIn this paper, we consider the asymptotic behavior of solutions to the p-system with time-dependent damping on the half-line R+=0,+∞, vt−ux=0,ut+pvx=−α/1+tλu with the Dirichlet boundary condition ux=0=0, in particular, including the constant and nonconstant coefficient damping. The initial data v0,u0x have the constant state v+,u+ at x=+∞. We prove that the solutions time-asymptotically converge to v+,0 as t tends to infinity. Compared with previous results about the p-system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to H3R+×H2R+. Our proof is based on the time-weighted energy method.http://dx.doi.org/10.1155/2020/3060867
collection DOAJ
language English
format Article
sources DOAJ
author Ran Duan
Mina Jiang
Yinghui Zhang
spellingShingle Ran Duan
Mina Jiang
Yinghui Zhang
Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
Advances in Mathematical Physics
author_facet Ran Duan
Mina Jiang
Yinghui Zhang
author_sort Ran Duan
title Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
title_short Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
title_full Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
title_fullStr Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
title_full_unstemmed Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping
title_sort boundary effect on asymptotic behavior of solutions to the p-system with time-dependent damping
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2020-01-01
description In this paper, we consider the asymptotic behavior of solutions to the p-system with time-dependent damping on the half-line R+=0,+∞, vt−ux=0,ut+pvx=−α/1+tλu with the Dirichlet boundary condition ux=0=0, in particular, including the constant and nonconstant coefficient damping. The initial data v0,u0x have the constant state v+,u+ at x=+∞. We prove that the solutions time-asymptotically converge to v+,0 as t tends to infinity. Compared with previous results about the p-system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to H3R+×H2R+. Our proof is based on the time-weighted energy method.
url http://dx.doi.org/10.1155/2020/3060867
work_keys_str_mv AT randuan boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping
AT minajiang boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping
AT yinghuizhang boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping
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