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Keywords:
nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle
nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle
Summary:
The nonhomogeneous backward Cauchy problem $$u_t +Au(t) = f(t),\quad u(T) = \varphi$$, 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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