Local boundary controllability in classes of differentiable functions for the wave equation

TL;DR

This paper extends the known boundary controllability of wave equations to specific classes of differentiable functions, broadening the scope of controllability results in wave dynamics.

Contribution

It generalizes the classical boundary controllability to differentiable function classes within wave-filled domains, enhancing theoretical understanding.

Findings

Established controllability in classes of differentiable functions

Extended boundary controllability results beyond $L_2$ spaces

Provided new theoretical insights into wave control in differentiable function spaces

Abstract

The well-known fact following from the Holmgren-John-Tataru uniqueness theorem is a local approximate boundary $L_2$-controllability of the dynamical system governed by the wave equation. Generalizing this result, we establish the controllability in certain classes of differentiable functions in the domains filled up with waves.