# Boundary feedback stabilizability of parabolic equations

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## Abstract

A parabolic equation defined on a bounded domain is considered, with input acting on the*boundary* expressed as a specified*feedback* of the solution. Both Dirichlet and mixed (in particular, Neumann) boundary conditions are treated. Algebraic conditions based on the finitely many unstable eigenvalues are given, ensuring the existence of*boundary* vectors, for which all the solutions to the*boundary* feedback parabolic equation decay exponentially to zero as*t*→+∞ in (essentially) the strongest possible space norm. A semigroup approach is employed.

## Keywords

Boundary Condition System Theory Mathematical Method Bounded Domain Parabolic Equation
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