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Published in:
1995 | OriginalPaper | Chapter
The Cauchy Problem
Authors : Ruth F. Curtain, Hans Zwart
Published in: An Introduction to Infinite-Dimensional Linear Systems Theory
Publisher: Springer New York
Included in: Professional Book Archive
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In Theorem 2.1.10 we saw that if A is the infinitesimal generator of a C0-semigroup T(t), the solution of the abstract homogeneous Cauchy initial value problem $$\begin{array}{*{20}{c}}{\dot z\left( t \right) = Az\left( t \right),}&{t \geqslant 0,}&{z\left( 0 \right) = {z_0} \in D\left( A \right)}\end{array}$$ is given by $$z\left( t \right) = T\left( t \right){z_0}.$$