Via Carleman estimates we prove uniqueness and continuous dependence results for an identification and strongly ill-posed linear integro-differential parabolic problem with the Dirichlet boundary condition, but with no initial condition. The additional information consists in a boundary linear integral condition involving the normal derivative of the temperature on the whole of the lateral boundary of the space-time domain.
Lorenzi, A. (2013). A strongly ill-posed integro-differential parabolic problem with integral boundary conditions. Mathematical Modelling and Analysis, 18(3), 395-414. https://doi.org/10.3846/13926292.2013.804891
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