Instability of Continuous Systems pp 376-378 | Cite as
Linear Dynamical Systems in Hilbert Space
Conference paper
Abstract
We consider the initial value problem: where u 0 and u(t), f(t) for 0 ≤ t ≤ T are elements of a Hilbert space H. T is arbitrary but fixed, A is a linear operator. The differentiation with respect to t is meant in the generalised sense.
$$\frac{{du}}{{dt}} - Au = f\left( t \right)$$
(1)
$$u\left( 0 \right) = {u_0}$$
(1)
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References
- 1.de Graaf, J., Peletier, L.A.: Rend. Sem. Mat. Univ. Padova (to be published).Google Scholar
- 2.Ladyshenskaya, O. A.: Dokl. Akad. Nank S.S.S.R. 102, 207 (1955).Google Scholar
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© Springer-Verlag, Berlin/Heidelberg 1971