Geodesic
A simple regularization method for the ill-posed evolution equation
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 85-95

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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.
DOI : 10.1007/s10587-011-0019-9
Classification : 35K05, 35K99, 47H10, 47J06
Keywords: nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle 
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Tuan, Nguyen Huy; Trong, Dang Duc. A simple regularization method for the ill-posed evolution equation. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 85-95. doi: 10.1007/s10587-011-0019-9

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