On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms

We study a terminal value parabolic system with nonlinear-nonlocal diffiusions. Firstly, we consider the issue of existence and ill-posed property of a solution. Then we introduce two regularization methods to solve the system in which the diffiusion coefficients are globally Lipschitz or locally Lipschitz under some a priori assumptions on the sought solutions. The existence, uniqueness and regularity of solutions of the regularized problem are obtained. Further- more, The error estimates show that the approximate solution converges to the exact solution in L2 norm and also in H1 norm. © 2021 American Institute of Mathematical Sciences. All rights reserved.