Abstract
In this paper, we study the questions of uniqueness and continuous dependence on the initial data for evolutionary equations of the form: d nu dt n = Mu, n = 1, 2, 3,…, n fixed, where M is a linear operator on a subdomain D of a Hilbert space and u: [0, T) → D is a vector valued function. M is either symmetric or skew symmetric and need not be bounded or even semibounded. The method of proof is based on the so called “weighted energy method.” The results can be applied to the study of improperly posed problems.
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