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Optimal control of the viscous Camassa-Holm equation. (English) Zbl 1154.49300
Summary: This paper studies the problem of optimal control of the viscous Camassa-Holm equation. The existence and uniqueness of weak solution to the viscous Camassa-Holm equation are proved in a short interval. According to variational method, optimal control theories and distributed parameter system control theories, we can deduce that the norm of solution is related to the control item and initial value in the special Hilbert space. The optimal control of the viscous Camassa-Holm equation under boundary condition is given and the existence of optimal solution to the viscous Camassa-Holm equation is proved.
MSC:
49J20Optimal control problems with PDE (existence)
35K57Reaction-diffusion equations
35B25Singular perturbations (PDE)
76D05Navier-Stokes equations (fluid dynamics)