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This paper dealswith the extinction and nonextinction properties of the fast diffusion equation of homogeneousDirichlet boundary condition in a bounded domain of RN with N > 2. For 0 < m < 1, under appropriate hypotheses, we show that m = p is the critical exponent of extinction for the weak solution. Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of - with homogeneous Dirichlet boundary. [ABSTRACT FROM AUTHOR]

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the -convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results. [ABSTRACT FROM AUTHOR]