The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations In this paper, we consider the Cauchy problem $$\begin{cases} u_{t}=\Delta(u^{m}), &x\in{}\mathbb{R}^{N}, t>0, N\geq3, \\ % ^^----- here u(x,0)=u_{0}(x), &x\in{}\mathbb{R}^{N}. \end{cases}$$ We will prove that: (i) for \$m_{c} Keywords:fast diffusion equations, Cauchy problem, continuous dependence on nonlinearityCategories:35K05, 35K10, 35K15