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# The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations

Published:2011-05-06
Printed: Sep 2012
• Jiaqing Pan,
Institute of Mathematics, Jimei University, Xiamen, 361021, P. R. China
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## Abstract

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 nonlinearity
 MSC Classifications: 35K05 - Heat equation 35K10 - Second-order parabolic equations 35K15 - Initial value problems for second-order parabolic equations

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