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A simple regularization method for the ill-posed evolution equation

Nguyen Huy Tuan, Dang Duc Trong (2011)

Czechoslovak Mathematical Journal

The nonhomogeneous backward Cauchy problem u t + A u ( t ) = f ( t ) , u ( T ) = ϕ , where A is a positive self-adjoint unbounded operator which has continuous spectrum and f is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.

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