This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Hömberg, DietmarYamamoto, Masahiro2016-12-162019-06-2820060946-8633https://doi.org/10.34657/2331https://oa.tib.eu/renate/handle/123456789/3282Motivated by the growing number of industrially important laser material treatments we investigate the controllability on a curve for a semilinear parabolic equation. We prove the local exact controllability and a global stability result in the twodimensional setting. As an application we consider the control of laser surface hardening. We show that our theory applies to this situation and present numerical simulations for a PID control of laser hardening. Moreover, the result of an industrial case study is presented confirming that the numerically derived temperature in the hot-spot of the laser can indeed be used as set-point for the machine-based process control.application/pdfeng510Exact controllabilityparabolic equationlaser material treatmentReport