Beschreibung:
<p>We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper L comma tau right-parenthesis">
<mml:semantics>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mi>L</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>τ<!-- τ --></mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:annotation encoding="application/x-tex">\left ( {L, \tau } \right )</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>, the corresponding semigroup generator generally admits <italic>no</italic> Riesz basis of eigenvectors. Very little information on the fractional powers of this generator is needed. In this sense our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a unified algebraic approach to the stabilization of a variety of parabolic boundary control systems.</p>