Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle
This article focuses on a one-dimensional nonlinear wave equation which is the Euler-Lagrange equation of a variational principle whose Lagrangian density involves linear terms and zero term as well as quadratic terms in derivatives of the field. We establish the global existence of weak solutio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/294/abstr.html |
| _version_ | 1811286499786752000 |
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| author | Yanbo Hu Guodong Wang |
| author_facet | Yanbo Hu Guodong Wang |
| author_sort | Yanbo Hu |
| collection | DOAJ |
| description | This article focuses on a one-dimensional nonlinear wave equation which
is the Euler-Lagrange equation of a variational principle whose Lagrangian
density involves linear terms and zero term as well as quadratic terms
in derivatives of the field. We establish the global existence of weak
solutions to its Cauchy problem by the method of energy-dependent coordinates
which allows us to rewrite the equation as a semilinear system and resolve
all singularities by introducing a new set of variables related to the energy. |
| first_indexed | 2024-04-13T03:01:04Z |
| format | Article |
| id | doaj.art-869af2d925c1493eaca438818de3065f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T03:01:04Z |
| publishDate | 2017-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-869af2d925c1493eaca438818de3065f2022-12-22T03:05:26ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-11-012017294,120Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principleYanbo Hu0Guodong Wang1 Hangzhou Normal Univ., Hangzhou, China Anhui Jianzhu Univ., Hefei, 230601, China This article focuses on a one-dimensional nonlinear wave equation which is the Euler-Lagrange equation of a variational principle whose Lagrangian density involves linear terms and zero term as well as quadratic terms in derivatives of the field. We establish the global existence of weak solutions to its Cauchy problem by the method of energy-dependent coordinates which allows us to rewrite the equation as a semilinear system and resolve all singularities by introducing a new set of variables related to the energy.http://ejde.math.txstate.edu/Volumes/2017/294/abstr.htmlNonlinear wave equationweak solutionsexistenceenergy-dependent coordinates |
| spellingShingle | Yanbo Hu Guodong Wang Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle Electronic Journal of Differential Equations Nonlinear wave equation weak solutions existence energy-dependent coordinates |
| title | Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle |
| title_full | Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle |
| title_fullStr | Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle |
| title_full_unstemmed | Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle |
| title_short | Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle |
| title_sort | global solutions to a one dimensional nonlinear wave equation derivable from a variational principle |
| topic | Nonlinear wave equation weak solutions existence energy-dependent coordinates |
| url | http://ejde.math.txstate.edu/Volumes/2017/294/abstr.html |
| work_keys_str_mv | AT yanbohu globalsolutionstoaonedimensionalnonlinearwaveequationderivablefromavariationalprinciple AT guodongwang globalsolutionstoaonedimensionalnonlinearwaveequationderivablefromavariationalprinciple |