A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain Omega ×O of R^(M+N)

In this paper, we deal with a strongly ill-posed second-order degenerate parabolic problem in the unbounded open set Omega × O ⊂ R^(M+N), related to a linear equation with unbounded coefficients, with no initial condition, but endowed with the usual Dirichlet condition on (0, T ) × ∂(Omega × O) and an additional condition involving the x-normal derivative on ×O, with being an open subset of. The purpose of this paper is twofold: to determine sufficient conditions on our data implying the uniqueness of the solution u to the boundary value problem and determine a pair of metrics with respect to which u depends continuously on the data. The results obtained for the parabolic problem are then applied to a similar problem for a convolution integrodifferential linear parabolic equation.