Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 70, pp. 1-8.
Title: Point rupture solutions of a singular elliptic equation
Authors: Huiqiang Jiang (Univ. of Pittsburgh, PA, USA)
Attou Miloua (Univ. of Pittsburgh, PA, USA)
Abstract:
We consider the elliptic equation
$$
\Delta u=f(u)
$$
in a region $\Omega\subset\mathbb{R}^2$, where f is a positive continuous
function satisfying
$$
\lim_{u\to 0^{+}}f(u) =\infty.
$$
Motivated by the thin film equations, a solution $u$ is said to be a point
rupture solution if for some $p\in\Omega$, $u(p) =0$ and
$u(p) >0$ in $\Omega\backslash\{ p\} $. Our main
result is a sufficient condition on f for the existence of radial point
rupture solutions.
Submitted May 2, 2012. Published March 13, 2013.
Math Subject Classifications: 49Q20, 35J60, 35Q35.
Key Words: Thin film; point rupture; radial solution; singular equation.