Duality for Evolutionary Equations With Applications to Null Controllability

Key Points

• This research aims to analyze duality in evolutionary equations and its relation to null controllability.
• Studied evolutionary equations in exponentially weighted spaces.
• Described the adjoint system which operates backward in time.
• Proved well-posedness for the adjoint system.
• Investigated applications of duality to null controllability.
• Successfully defined the adjoint system for evolutionary equations.
• Demonstrated well-posedness of the adjoint system.
• Introduced new notions of null controllability.