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Optimal control of the viscous weakly dispersive Degasperis-Procesi equation. (English) Zbl 1181.35199

Summary: We study the optimal control problem for the viscous weakly dispersive Degasperis-Procesi equation. We deduce the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Then, according to optimal control theory and distributed parameter system control theory, the optimal control of the viscous weakly dispersive Degasperis-Procesi equation under boundary conditions is given and the existence of an optimal solution to the viscous weakly dispersive Degasperis-Procesi equation is proved.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D55 Flow control and optimization for incompressible viscous fluids
93C20 Control/observation systems governed by partial differential equations
76M10 Finite element methods applied to problems in fluid mechanics
49J15 Existence theories for optimal control problems involving ordinary differential equations
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