Null Controllability for Degenerate Parabolic Operators

Fleming-Viot diffusion processevolution of genetic types in a populationu t − Tr ( A(x)∇ 2 u ) = · · ·in O = {(x 1 , x 2 ) ∈ R 2 | x i ∈]0, 1[ , x 1 + x 2 ≤ 1}❅❅❅❅O ❅❅❅withA(x 1 , x 2 ) =(x1 (1 − x 1 ) −x 1 x 2−x 1 x 2 x 2 (1 − x 2 ))notice det A(x 1 , x 2 ) = x 1 x 2 (1 − x 1 − x 2 ) = 0 on ∂O