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ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 12, pp. 1697–1704. c Pleiades Publishing, Ltd., 2007. Original Russian Text c V.A. Il’in, E.I. Moiseev, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 12, pp. 1655–1663. PARTIAL DIFFERENTIAL EQUATIONS Optimal Boundary Control by an Elastic Force at One End of a String with the Other End Being Free for an Arbitrary Sufficiently Large Time Interval V. A. Il’in and E. I. Moiseev Moscow State University, Moscow, Russia Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia Received July 23, 2007 DOI: 10.1134/S0012266107120099 We generalize the method in [1, 2] to the optimization of the boundary control realized as an elastic force at one end x = 0 of the string and bringing the vibration process, described a generalized solution u(x, t) of the wave equation u (x, t) − u (x, t)= 0 (1) tt xx with the second end x = l being free, from an arbitrary given initial state {u(x, 0) = ϕ(x),u (x, 0) = ψ(x)} (2) to an arbitrary given terminal state u(x, T)= ϕˆ(x),u (x, T)= ψ(x) (3) for an arbitrarily large time interval T . Following [1, 2], in the rectangle
Differential Equations – Springer Journals
Published: Mar 25, 2007
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