The approximating character on nonlinearities of solutions of Cauchy problem for a singular diffusion equation
Pan, Jiaqing
Osaka J. Math., Tome 45 (2008) no. 1, p. 909-919 / Harvested from Project Euclid
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In this paper, we consider the Cauchy problem \begin{equation*} \left\{ \begin{array}{@{}ll@{}} u_{t}=(u^{m-1}u_{x})_{x}, & x \in \mathbb{R}{,}\ t>0{,}\ {-1} < m \leq 1,\\ u(x,0)=u_{0}, & x \in \mathbb{R}. \end{array} \right. \end{equation*} We will prove that: \begin{enumerate}[1)] \item $|u(x,t,m)-u(x,t,m_{0})|\to 0$ uniformly on $[-l,l]\times[\tau,T]$ as $m \to m_{0}$ for any given $l > 0$, $0<\tau
Publié le : 2008-12-15
Classification:  35K05,  35K10,  35K15 
@article{1227708825,
     author = {Pan, Jiaqing},
     title = {The approximating character on nonlinearities of solutions of Cauchy problem for a singular diffusion equation},
     journal = {Osaka J. Math.},
     volume = {45},
     number = {1},
     year = {2008},
     pages = { 909-919},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227708825}
}

Pan, Jiaqing. The approximating character on nonlinearities of solutions of Cauchy problem for a singular diffusion equation. Osaka J. Math., Tome 45 (2008) no. 1, pp.  909-919. http://gdmltest.u-ga.fr/item/1227708825/