LAUSR

We consider in this paper the maximization problem for the quantity $\int_\Omega u(T, x)dx with respect to $u_0 $, where $u$ is the solution of a given reaction-diffusion equation. This problem is motivated by biological conservation questions. We show the existence of a maximizer and derive optimality conditions through an adjoint problem. We have to face regularity issues since non-smooth initial data could give a better result than smooth ones. We then derive an algorithm enabling to approximate the maximizer and discuss some open problems.