Showalter regularization of a singularly perturbed PDE

摘要

In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Viewing it as an ill-posed problem, Showalter's regularization method is applied to approximate the solution. Convergence of the regularized solution to the original is proved. A numerical example has been included for illustrating the method.