Uniqueness of the Solutions of (u sub t)-(Delta(thi(u))=0 with Initial Datum a Measure.

Abstract
The uniqueness property for solutions of an initial-value problem turns out to be a fundamental tool which interacts with many other questions of a qualitative nature. For an evolution equation that is supposed to serve as a model for a natural phenomenon, it is often crucial if one wants the model to be credible. The variety of these applications explains the abundant literature concerning uniqueness for such problems. This paper is a new contribution to this question. It deals with the case when the initial datum is a measure, (E) being understood in the sense of distributions. Thanks to this general setting, it recovers most of the previous results and takes into account a larger number of physical models. But its main interest comes from the fact that it solves the 'right' uniqueness question in a form which arises in many other related questions. For instance the study of the asymptotic behavior of the solutions of (E) can be reduced to this type of a uniqueness problem with a Dirac mass as initial datum.

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