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

Abstract

We study for the first time the ill-posed backward problem for a contaminated nonlinear predatorprey 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 L 2 − and H 1 −norms in Theorems 2 and 3, respectively. Furthermore, numerical simulations are performed to illustrate the accuracy and stability of the regularized solution.

Regularization of the backward stochastic heat conduction problem

“…The deterministic model of Problem (1), i.e., when f (t) Ẇ is omitted, commonly known as the backward heat conduction problem (BHCP) has been extensively studied in the literature over the last few decades, see e.g. [2,3,4,5,9,12,13,15,16] to mention only a few. The BHCP arises in several practical areas such as heat transfer and image processing, [1,9].…”