TY - JOUR
T1 - On the Optimal Control Problem of Laser Surface Hardening
AU - Gupta , N.
AU - Nataraj , N.
AU - Pani , A. K.
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 667
EP - 680
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/745.html
KW - Laser surface hardening of steel, semilinear parabolic equation, ODE with non-differentiable forcing function, regularized Heaviside function, regularised problem, convergence with respect to regularization parameter, numerical experiments.
AB - <p style="text-align: justify;">We discuss an optimal control problem of laser surface hardening
of steel which is governed by a dynamical system consisting of a semilinear parabolic
equation and an ordinary differential equation with a non differentiable
right hand side function $f_+$. To avoid the numerical and analytic difficulties
posed by $f_+$, it is regularized using a monotone Heaviside function and the
regularized problem has been studied in literature. In this article, we establish
the convergence of solution of the regularized problem to that of the original
problem. The estimates, in terms of the regularized parameter, justify the existence
of solution of the original problem. Finally, a numerical experiment is
presented to illustrate the effect of regularization parameter on the state and
control errors.</p>