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A strongly ill-posed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$

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  • Via Carleman's estimates we prove uniqueness and continuous dependence results for a severely ill-posed linear integro-differential singular parabolic problems without initial conditions.
    Mathematics Subject Classification: Primary: 30R35; Secondary: 35K20, 34G10, 45N05, 45Q05.

    Citation:

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    A. Lorenzi, Linear integro-differential Schrödinger and plate problems without initial conditions, Appl. Math. Optim., 67 (2013), 391-418.doi: 10.1007/s00245-013-9192-6.

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    A. Lorenzi, Recovering a t-function in a strongly ill-posed integro-differential parabolic problem with integral boundary conditions, to appear in Mathematical Modelling and Analysis.

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    A. Lorenzi and L. Lorenzi, A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain $\Omega\times \mathcal O$ of $\mathbb R^{M+N}$, Inverse Problems, 29 (2013), 025007, 22 pp.doi: 10.1088/0266-5611/29/2/025007.

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    A. Lorenzi and F. Messina, Unique continuation and continuous dependence results for a strongly ill-posed integro-differential parabolic problem, J. Inverse Ill-Posed Probl., 20 (2012), 615-636.doi: 10.1515/jip-2012-0032.

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    A. Lorenzi and M. Yamamoto, Continuous dependence and uniqueness for a strongly ill-posed problem for linear integrodifferential parabolic equations, in progress.

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