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We prove uniqueness and continuous dependence results for a severely ill-posed linear integrodifferential boundary-value parabolic problem with  no  initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domain   .

journal of inverse and ill-posed problems

Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator