REVERSE CONVOLUTION INEQUALITIES AND APPLICATIONS TO INVERSE HEAT SOURCE PROBLEMS

Abstract

We introduce reverse convolution inequalities obtained recently and at the same time, we give new type reverse convolution inequalities and their important applications to in-verse source problems. We consider the inverse problem of determining f (t), 0 < t 0 from the observation u(x 0 , t), 0 < t < T , at a remote point x 0 away from the support of ϕ. Under an a priori assumption that f changes the signs at most N -times, we give a conditional stability of Hölder type, as an example of applications.