Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592031 | Journal of Functional Analysis | 2008 | 27 Pages |
Abstract
In this paper we consider a two-dimensional diffusion equation on the closed right halfspace satisfying a boundary condition for which the minimum principle fails. As a consequence, the associated Cauchy initial value problem fails to be well-posed. In particular, solutions need not exist and, when they do exist, they may do so for only a finite length of time. Among other things, we provide a necessary and sufficient condition on the initial data in order that the solution exist for all time and remain non-negative.
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