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In this paper the Cauchy problem for nonlinear parabolic equation is investigated. We prove that the Cauchy problem has one nontrivial solution u(t, r) in the form u(t, r) = v(t)ω(r) ∈ C([0, 1)L 2 ([r 0 , ∞))) for which lim t−→1 ||u|| L 2 ([r 0 ,∞))) = ∞, where r = |x|, r 0 ≥ 1 is arbitrary chosen and fixed. Also, we prove that the solution map is not uniformly continuous. 1991 Mathematics Subject Classification. 35.doi:10.4310/dpde.2009.v6.n1.a1 fatcat:7pywyqhweffklftr2mm2v4fp4a