Regularization of a terminal value nonlinear diffusion equation with conformable time derivative

Abstract

For an inverse nonlinear diffusion equation with conformable time derivative, we study the ill-posed property in the sense of Hadamard. To obtain a stable numerical solution, we propose two regularization methods. The results of existence and uniqueness, regularity and stability of the regularized problem are obtained. We also show that the corresponding regularized solutions converge to the sought solution strongly in $L^2\left({ℝ}^d\right)$ uniformly under some a priori assumptions on the solution.