boundary behavior of solutions to a singular dirichlet problem with a nonlinear convection
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2015
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Abstract
In this article we analyze the exact boundary behavior of
solutions to the singular nonlinear Dirichlet problem
$$\displaylines{
-\Delta u=b(x)g(u)+\lambda|\nabla u|^q+\sigma, \quad u>0, \; x \in \Omega,\cr
u\big|_{\partial \Omega}=0,
}$$
where $\Omega$ is a bounded domain with smooth
boundary in $\mathbb{R}^N$, $q\in (0, 2]$, $\sigma>0$,
$\lambda> 0$, $g\in C^1((0,\infty), (0,\infty))$,
$\lim_{s \to 0^+}g(s)=\infty$, $g$ is decreasing on $(0, s_0)$
for some $s_0>0$, $b \in C_{\rm loc}^{\alpha}({\Omega})$ for some
$\alpha\in (0, 1)$, is positive in $\Omega$, but may be vanishing or
singular on the boundary. We show that $\lambda |\nabla u|^q$
does not affect the first expansion of classical solutions near the
boundary.
| Reference Key |
li2015electronicboundary
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|---|---|
| Authors | ;Bo Li;Zhijun Zhang |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2015 |
| DOI |
DOI not found
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| URL | |
| Keywords | Keywords not found |
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