Abstract :
The initialization problem for Burgers′ equation with viscosity is formulated as an optimal control problem. The existence of a solution of this problem is established directly, and the optimality system is obtained. From this system, we deduce regularity properties of the optimal initial conditions. These regularity properties imply the compactness of the set U0 of optimal initial conditions. By introducing sufficiency conditions for optimality, we deduce conditions under which there are in fact finitely many elements in the set U0. Finally, we determine conditions that imply the optimality system has a unique solution. It then follows that there is only one element in U0.
