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Optimal Control of Laser Hardening

Abstract : We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume fractions of the occuring phases. Existence, regularity and stability results are discussed. Since the resulting hardness can be estimated by the volume fraction of martens­ite, we formulate the problem of surface hardening in terms of an optimal control problem. To avoid surface melting, which would decrease the workpiece's quality, state constraints for the temperature are included. We prove differentiability of the solution operator and derive necessary conditions for optimality.
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Submitted on : Wednesday, May 24, 2006 - 1:06:48 PM
Last modification on : Friday, February 4, 2022 - 3:23:48 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:49:07 PM


  • HAL Id : inria-00073520, version 1



Dietmar Hömberg, Jan Sokolowski. Optimal Control of Laser Hardening. [Research Report] RR-3168, INRIA. 1997, pp.23. ⟨inria-00073520⟩



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