We consider optimal control problems associated to generally non-well posed Cauchy in a general framework. Firstly, we approximate the ill-posed problem with family of well-posed one and show that solutions latter converge former one. Secondly, investigate minimization approximated state equation. prove existence uniqueness minimizers characterize optimality systems. Finally, subjected equation...

Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...