Discrete non standard formulation of PDE inverse problems

Abstract In this paper, we are interested in the computation of the unknown initial state for the simulation and prediction of PDE systems where the solution measures are partially known over a time interval. Such a problem is usually solved by an ill-posed optimal control problem. Based on an appropriate collocation approximation, we obtain a discrete inverse problem. To solve this problem, a non-standard discrete approach is used. This allows to obtain a transformation of the original problem into a well-posed ones based on the zero controllability of a discrete system. The desired control is then calculated as well as the discrete approximation of the initial state values. Mathematics Subject Classification. 35K55; 35J60; 80A22.