Semidiscrete finite element approximation of time optimal control problems for semilinear heat equations with nonsmooth initial data

This paper is devoted to the study of semidiscrete finite element approximation of time optimal control problem governed by semilinear heat equation with nonsmooth initial data. When the control is acted locally, an error estimate for the optimal time is obtained by making use of the approximation results for the equations. Moreover, with the help of Pontryagin's maximum principle and the unique continuation property for the heat equation, a better error estimate for the optimal time can be derived when the control is acted globally into the state equation.