An adaptive numerical method for the wave equation with a nonlinear boundary condition
We develop an efficient numerical method for studying the existence and non-existence of global solutions to the initial-boundary value problem {gather*} u_{tt}=u_{xx}quad 0<x<infty,; t>0, -u_{x}(0,t)=h(u(0,t)) quad t>0, u(x,0)=f(x),quad u_{t}(x,0)=g(x) quad 0<x<infty. end{gather*}...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/10/a3/abstr.html |
| _version_ | 1818566736849403904 |
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| author | Azmy S. Ackleh Keng Deng Joel Derouen |
| author_facet | Azmy S. Ackleh Keng Deng Joel Derouen |
| author_sort | Azmy S. Ackleh |
| collection | DOAJ |
| description | We develop an efficient numerical method for studying the existence and non-existence of global solutions to the initial-boundary value problem {gather*} u_{tt}=u_{xx}quad 0<x<infty,; t>0, -u_{x}(0,t)=h(u(0,t)) quad t>0, u(x,0)=f(x),quad u_{t}(x,0)=g(x) quad 0<x<infty. end{gather*} The results by this numerical method corroborate the theory presented in cite{AD}. Furthermore, they suggest that blow-up can occur for more general nonlinearities $h(u)$ with weaker conditions on the initial data $f$ and $g$. |
| first_indexed | 2024-12-14T01:57:27Z |
| format | Article |
| id | doaj.art-3e9dc639841741e5b81712b9b15c7064 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:57:27Z |
| publishDate | 2003-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3e9dc639841741e5b81712b9b15c70642022-12-21T23:21:08ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-02-01Conference102331An adaptive numerical method for the wave equation with a nonlinear boundary conditionAzmy S. AcklehKeng DengJoel DerouenWe develop an efficient numerical method for studying the existence and non-existence of global solutions to the initial-boundary value problem {gather*} u_{tt}=u_{xx}quad 0<x<infty,; t>0, -u_{x}(0,t)=h(u(0,t)) quad t>0, u(x,0)=f(x),quad u_{t}(x,0)=g(x) quad 0<x<infty. end{gather*} The results by this numerical method corroborate the theory presented in cite{AD}. Furthermore, they suggest that blow-up can occur for more general nonlinearities $h(u)$ with weaker conditions on the initial data $f$ and $g$.http://ejde.math.txstate.edu/conf-proc/10/a3/abstr.htmlTime-adaptive numerical methodblow-up timeblow-up rate. |
| spellingShingle | Azmy S. Ackleh Keng Deng Joel Derouen An adaptive numerical method for the wave equation with a nonlinear boundary condition Electronic Journal of Differential Equations Time-adaptive numerical method blow-up time blow-up rate. |
| title | An adaptive numerical method for the wave equation with a nonlinear boundary condition |
| title_full | An adaptive numerical method for the wave equation with a nonlinear boundary condition |
| title_fullStr | An adaptive numerical method for the wave equation with a nonlinear boundary condition |
| title_full_unstemmed | An adaptive numerical method for the wave equation with a nonlinear boundary condition |
| title_short | An adaptive numerical method for the wave equation with a nonlinear boundary condition |
| title_sort | adaptive numerical method for the wave equation with a nonlinear boundary condition |
| topic | Time-adaptive numerical method blow-up time blow-up rate. |
| url | http://ejde.math.txstate.edu/conf-proc/10/a3/abstr.html |
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