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The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper, we consider the Cauchy problem

We will prove that
(i) for ${{m}_{c}}\,<\,m,\,{{m}_{0}}\,<\,1,\,\left| u(x,\,t,m)-u(x,\,t,{{m}_{0}}) \right|\,\to \,0$ as
$m\,\to \,{{m}_{0}}$ uniformly on every compact subset of
${{\mathbb{R}}^{N}}\,\times \,{{\mathbb{R}}^{+}}$, where
${{m}_{c}}\,=\,\frac{{{(N-2)}_{+}}}{N}$;
(ii) there is a ${{C}^{*}}$ that explicitly depends on
$m$ such that

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- Copyright © Canadian Mathematical Society 2012