On a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity terms

In this article, we are interested in investigating the nonlocal nonlinear reaction–diffusion system with final conditions. This problem is called backward time problem, or terminal value which understood as redefining previous distributions when distribution data at observation known. There three main goals presented paper. First, prove that ill-posed (often unstable property) sense of Hadamard. Our next propose to provide a modified quasi-reversibility model stabilize problem. Using some techniques and tools Faedo–Galerkin method, existence unique weak solution regularized Further, investigate error estimates between sought L2(Ω)− H1(Ω)− norms. The aim paper give numerical results demonstrate our method useful effective.