The initial-value problem is studied for evolution equations in Hilbert AMS(MOS) 78712.Sponsored by th., I!!The responsibility for the wording and views expressed in this descriptive summary lies with MRC, and not with the authors of this report.

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Í u, -div(|Z>u|"-2Z>«) \ u(x,0) = u0(x), Abstract. We consider the Cauchy problem i) = 0 in R* x (0, oo), p > 2, x€RN, and discuss existence of solutions in some strip St a HN x (0, T), 0 < T < oo , in terms of the behavior of x -* uo(x) as |x| -► oo . The results obtained are optimal in the class of nonnegative locally bounded solutions, for which a Harnack-type inequality holds. Uniqueness is shown under the assumption that the initial values are taken in the sense of ¿^.(R-^).

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