In this paper, we apply a logarithmic approximation introduced by Boussetila and Rebbani in order to study an ill-posed Cauchy problem in Banach space. The proposed method induces a well-posed problem whose approximation parameter yields continuous dependence on modeling. Throughout, properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in L p (R), 1<p<∞.
All Science Journal Classification (ASJC) codes
- Applied Mathematics