Identification of the initial population of a nonlinear predator-prey system backwards in time

We study for the first time the ill-posed backward problem for a contaminated nonlinear predator-prey system whose velocities of migration depend on the total average populations in the considered space domain. We propose a new regularized problem for which we are able to prove its unique solvability in Theorem 1. Moreover, under some mild assumptions on the true solution, we give useful and rigorous error estimates and convergence rates in both the L² –and H² – norms in Theorems 2 and 3, respectively. Furthermore, numerical simulations are performed to illustrate the accuracy and stability of the regularized solution.