Regularization of backward parabolic equations in Banach spaces

Abstract

Abstract. The ill-posed backward parabolic equation with a densely defined linear operator A such that generates an analytic semigroup in a Banach space X and being given is stabilized by the Tikhonov regularization method and by the well-posed non-local boundary value problem A priori and a posteriori parameter choice rules for these regularization methods are suggested which yield the error estimate for all , where are computable constants, E is a bound for and is a defined harmonic function.