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In this paper we deal with a strongly ill-posed second-order degenerateparabolic problem in the unbounded open set $\Omega\times {\mathcal O}\subset\mathbb R^{M+N}$, related to a linear equation with unbounded coefficients,with no initial condition, but endowed with the usual Dirichlet condition on$(0,T)\times \partial(\Omega\times {\mathcal O})$ and an additional conditioninvolving the $x$-normal derivative on $\Gamma\times {\mathcal O}$, $\Gamma$being an open subset of $\Omega$.  The task of this paper is twofold: determining sufficient conditions on ourdata implying the uniqueness of the solution $u$ to the boundary value problemas well as determining a pair of metrics with respect of which $u$ dependscontinuously on the data.  The results obtained for the parabolic problem are then applied to a similarproblem for a convolution integrodifferential linear parabolic equation.

inverse problems

A strongly ill-posed problem for a degenerate parabolic equation with  unbounded coefficients in an unbounded domain $\Omega\times {\mathcal O}$ of  $\R^{M+N}$