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**1 - 2**of**2**### Time optimal control problem of the wave equation

"... ABSTRACT To obtain a control function which puts the wave equation in an unknown min-imum time into a stationary regime is considered is considered. Using an embedding method, the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of posit ..."

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ABSTRACT To obtain a control function which puts the wave equation in an unknown min-imum time into a stationary regime is considered is considered. Using an embedding method, the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated by a finite dimensional linear programming (LP) problem. The nearly optimal control is constructed from the solution of the final LP problem. To find the lower bound of the optimal time a search algorithm is proposed. Some examples demonstrate the effectiveness of the method.

### A numerical scheme for Fredholm integral equations

"... Abstract. A different numerical method for nonlinear Fredholm integral equations of the second kind with the continuous kernel is considered. The main idea is to convert the integral equation problem into an optimization problem. Then by using an embedding method, the class of admissible trajectorie ..."

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Abstract. A different numerical method for nonlinear Fredholm integral equations of the second kind with the continuous kernel is considered. The main idea is to convert the integral equation problem into an optimization problem. Then by using an embedding method, the class of admissible trajectories is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a finite dimensional linear programming (LP) problem. Some examples demonstrate the effectiveness of the method.