Designing for optimal energy absorption. II: The damped wave equation. (English) Zbl 0992.93037
Desch, W. (ed.) et al., Control and estimation of distributed parameter systems. International conference in Vorau, Austria, July 14-20, 1996. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 126, 103-109 (1998).
Summary: We consider the wave equation in a bounded domain with zero Dirichlet data and damping proportional to velocity and pose the problem of minimizing, with respect to damping, the maximum, over all initial data of unit energy, of the infinite time integral of the instantaneous energy. We show the minimum to exist over those dampings that uniformly avoid zero and infinity. We provide an exact minimum over the class of constant dampings and proceed to show it to be a critical point over the class of bounded dampings.
Part I, cf. ASME J. Vib. Acoust. 120, No. 2, 339-345 (1998), will not be reviewed.
For the entire collection see [Zbl 0889.00041].
Part I, cf. ASME J. Vib. Acoust. 120, No. 2, 339-345 (1998), will not be reviewed.
For the entire collection see [Zbl 0889.00041].
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 35L05 | Wave equation |
| 93D15 | Stabilization of systems by feedback |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
