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The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations |
Canad. Math. Bull. 55(2012), 623-631
Published:2011-05-06
Printed: Sep 2012
Printed: Sep 2012
- Jiaqing Pan,
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 |