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/'(§) > 0 for §> 0, where ' = dld^\ (A2) /ofl" is locally Lipschitz continuous on [a(0),^°). (A3) UQ(X) E L(£2)\ UQ(X) > 0 in Q\ the support of MO(JC) contains an open nonempty subset of Q. These conditions guarantee the unique existence of local (in time) solution u(x,t)>Q which satisfies (0.1) ~ (0.3) in a weak sense (cf. e.g., [1],[2],[12] and [13]). In the following we do not enter into this existence problem. The definition

On blow-up of solutions for quasilinear degenerate parabolic equations