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Volume 3, Issue 1
Periodic Solutions of Nonlinear Wave Equations with Dissipative Boundary Conditions

Qin Tiehu

DOI: 10.4208/aamm.10-m1030

J. Part. Diff. Eq.,3(1990),pp.1-12

Published online: 1990-03

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  • Abstract
Applying Nash-Moser's implicit function theorem, the author proves the existence of periodic solution to nonlinear wave equation u_{tt} - u_{xx} + εg(t, x, u, u_t, u_x, u_{tt}, u_{tx}, u_{xx}) = 0 with a dissipative boundary condition, provided ε is sufficiently small.
  • Keywords

Nonlinear wave equation time periodic solution dissipative boundary condition

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@Article{JPDE-3-1, author = {Qin Tiehu}, title = {Periodic Solutions of Nonlinear Wave Equations with Dissipative Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {1}, pages = {1--12}, abstract = { Applying Nash-Moser's implicit function theorem, the author proves the existence of periodic solution to nonlinear wave equation u_{tt} - u_{xx} + εg(t, x, u, u_t, u_x, u_{tt}, u_{tx}, u_{xx}) = 0 with a dissipative boundary condition, provided ε is sufficiently small.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/aamm.10-m1030}, url = {http://global-sci.org/intro/article_detail/jpde/5786.html} }
TY - JOUR T1 - Periodic Solutions of Nonlinear Wave Equations with Dissipative Boundary Conditions AU - Qin Tiehu JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 12 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1030 UR - https://global-sci.org/intro/article_detail/jpde/5786.html KW - Nonlinear wave equation KW - time periodic solution KW - dissipative boundary condition AB - Applying Nash-Moser's implicit function theorem, the author proves the existence of periodic solution to nonlinear wave equation u_{tt} - u_{xx} + εg(t, x, u, u_t, u_x, u_{tt}, u_{tx}, u_{xx}) = 0 with a dissipative boundary condition, provided ε is sufficiently small.
Qin Tiehu. (1990). Periodic Solutions of Nonlinear Wave Equations with Dissipative Boundary Conditions. Journal of Partial Differential Equations. 3 (1). 1-12. doi:10.4208/aamm.10-m1030
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