Geodesic
A simple regularization method for the ill-posed evolution equation
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 85-95 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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