DOIAbstract
AbstractWe consider the backward parabolic equation{ut+Au=f(t,u(t)),0<t<T,u(T)=g, where A is a positive unbounded operator and f is a nonlinear function satisfying a Lipschitz condition, with an approximate datum g. The problem is severely ill-posed. Using the truncation method we propose a regularized solution which is the solution of a system of differential equations in finite dimensional subspaces. According to some a priori assumptions on the regularity of the exact solution we obtain several explicit error estimates including an error estimate of Hölder type for all t∈[0,T]. An example on heat equations and numerical experiments are given
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