Bilinear optimal control for a wave equation with viscous damping. (English) Zbl 0976.49005

Lenhart, Suzanne; Liang, Min

Houston J. Math. 26, No. 3, 575-595 (2000).

The paper considers an optimal control problem for the wave equation \[ y_{tt}= \Delta y-k(t) y_t- q(x)y+ f,\quad (x,t)\in \Omega\times (0,T), \] with viscous damping and zero Dirichlet boundary conditions. The coefficient \(k\) plays the role of control. Under some assumptions on \(q\), \(f\) and initial conditions the differentiability of the mapping \(k\to y(k)\), the existence of an optimal control and the maximum principle are proved.

Reviewer: Uldis Raitums (Riga)

MSC:

49J20	Existence theories for optimal control problems involving partial differential equations
35L05	Wave equation
49K20	Optimality conditions for problems involving partial differential equations

Keywords:

necessary optimality conditions; optimal control; wave equation; viscous damping; existence; maximum principle