Optimal solution for the viscous nonlinear dispersive wave equation. (English) Zbl 1310.76037
Summary: In this paper, we study the optimal control problem for the viscous nonlinear dispersive wave equation. We first prove the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Furthermore, the existence of an optimal solution to the viscous nonlinear dispersive wave equation is proved.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76D33 | Waves for incompressible viscous fluids |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35D30 | Weak solutions to PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
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