March 3, 2026Open Access

Duality for evolutionary equations with applications to null controllability

Key Points

Null controllability is addressed through duality in evolutionary equations, offering insights into system dynamics.
A well-posedness proof is established for the adjoint system of exponential spaces introduced by Picard.
The research benefits from detailed descriptions of the backward-time behavior of the adjoint system for effective analysis.
Exploring these concepts may enhance control strategies in various mathematical and engineering applications.

Abstract

We study evolutionary equations in exponentially weighted (Formula presented.) -spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the (Formula presented.) -adjoint system, which turns out to describe a system backwards in time. We prove well-posedness for the (Formula presented.) -adjoint system. We then apply the obtained duality to introduce and study notions of null controllability for evolutionary equations.

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Authors

Andreas Buchinger

Christian Seifert

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Duality for evolutionary equations with applications to null controllability

Key Points

Abstract

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Discussion

Authors

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Citation Network

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