Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
IMPACT FACTOR 2017: 0.941
5-year IMPACT FACTOR: 0.953
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Mathematical Citation Quotient (MCQ) 2017: 0.49
We prove regularization for a certain ill-posed parabolic evolution problem in a Banach space X by obtaining Hölder-continuous dependence of its solution on modeling. In particular, we consider the generally ill-posed problem , , with initial data , in X where is the infinitesimal generator of a bounded holomorphic semigroup of angle on X, and for each with for . Assuming there exists a solution of the problem adhering to certain stabilizing conditions, we approximate by the solution of an approximate well-posed problem. We then use this estimate to prove the existence of a family of regularizing operators for the given ill-posed problem. The theory has applications to the backwards heat equation and other ill-posed partial differential equations in , , with time-dependent coefficients.