Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients
In this article, we study the hyperbolic problem $$ K(x,t)u_{tt} - sum_{j=1}^nleft(a(x,t)u_{x_j} ight) + F(x,t,u,abla u) = 0 $$ coupled with boundary conditions $$u=0,quadhbox{on }Gamma_1,, quad {partial u overpartialu} + Beta(x)u_t =0quadhbox{ on }Gamma_0,.$$ Here the variable $x$ belongs to a boun...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
1998-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1998/08/abstr.html |
| _version_ | 1818393966727397376 |
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| author | Marcelo M. Cavalcanti V. N. Domingos Cavalcanti Juan A. Soriano |
| author_facet | Marcelo M. Cavalcanti V. N. Domingos Cavalcanti Juan A. Soriano |
| author_sort | Marcelo M. Cavalcanti |
| collection | DOAJ |
| description | In this article, we study the hyperbolic problem $$ K(x,t)u_{tt} - sum_{j=1}^nleft(a(x,t)u_{x_j} ight) + F(x,t,u,abla u) = 0 $$ coupled with boundary conditions $$u=0,quadhbox{on }Gamma_1,, quad {partial u overpartialu} + Beta(x)u_t =0quadhbox{ on }Gamma_0,.$$ Here the variable $x$ belongs to a bounded region of ${Bbb R}^n$, whose boundary is partitioned into two disjoint sets $Gamma_0,Gamma_1$. |
| first_indexed | 2024-12-14T05:53:43Z |
| format | Article |
| id | doaj.art-a8b8197cf0c7426088db7cff3d9d8a62 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T05:53:43Z |
| publishDate | 1998-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-a8b8197cf0c7426088db7cff3d9d8a622022-12-21T23:14:39ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911998-03-01199808121Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficientsMarcelo M. CavalcantiV. N. Domingos CavalcantiJuan A. SorianoIn this article, we study the hyperbolic problem $$ K(x,t)u_{tt} - sum_{j=1}^nleft(a(x,t)u_{x_j} ight) + F(x,t,u,abla u) = 0 $$ coupled with boundary conditions $$u=0,quadhbox{on }Gamma_1,, quad {partial u overpartialu} + Beta(x)u_t =0quadhbox{ on }Gamma_0,.$$ Here the variable $x$ belongs to a bounded region of ${Bbb R}^n$, whose boundary is partitioned into two disjoint sets $Gamma_0,Gamma_1$.http://ejde.math.txstate.edu/Volumes/1998/08/abstr.htmlBoundary stabilizationasymptotic behaviour. |
| spellingShingle | Marcelo M. Cavalcanti V. N. Domingos Cavalcanti Juan A. Soriano Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients Electronic Journal of Differential Equations Boundary stabilization asymptotic behaviour. |
| title | Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients |
| title_full | Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients |
| title_fullStr | Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients |
| title_full_unstemmed | Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients |
| title_short | Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients |
| title_sort | existence and boundary stabilization of a nonlinear hyperbolic equation with time dependent coefficients |
| topic | Boundary stabilization asymptotic behaviour. |
| url | http://ejde.math.txstate.edu/Volumes/1998/08/abstr.html |
| work_keys_str_mv | AT marcelomcavalcanti existenceandboundarystabilizationofanonlinearhyperbolicequationwithtimedependentcoefficients AT vndomingoscavalcanti existenceandboundarystabilizationofanonlinearhyperbolicequationwithtimedependentcoefficients AT juanasoriano existenceandboundarystabilizationofanonlinearhyperbolicequationwithtimedependentcoefficients |