Geodesic
Point rupture solutions of a singular elliptic equation
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the elliptic equation $$ \Delta u=f(u) $$ in a region $$ \lim_{u\to 0^{+}}f(u) =\infty. $$ 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.
Classification : 49Q20, 35J60, 35Q35
Keywords: thin film, point rupture, radial solution, singular equation 
@article{EJDE_2013__2013__a24,
     author = {Jiang, Huiqiang and Miloua, Attou},
     title = {Point rupture solutions of a singular elliptic equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a24/}
}
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Jiang, Huiqiang; Miloua, Attou. Point rupture solutions of a singular elliptic equation. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a24/