Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

Abstract

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Holder type and propose a regularization method with error estimates of Holder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.