In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, interpret as inverse problem, and therefore a controllability problem. This point of view induces regularization method that makes it possible, on one hand, to characterize existence regular solution On other possible obtain singular optimality system optimal control, without resorting any addi...