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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3060867 |
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| author | Ran Duan Mina Jiang Yinghui Zhang |
| author_facet | Ran Duan Mina Jiang Yinghui Zhang |
| author_sort | Ran Duan |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-fcc419a37e0740188db082583c9dd439 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-fcc419a37e0740188db082583c9dd4392025-02-03T01:27:25ZengWileyAdvances 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/3060867 |
| work_keys_str_mv | AT randuan boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping AT minajiang boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping AT yinghuizhang boundaryeffectonasymptoticbehaviorofsolutionstothepsystemwithtimedependentdamping |