Existence and asymptotic behavior for a singular parabolic equation

Author	dc.contributor.author	Dávila, Juan
Author	dc.contributor.author	Montenegro, Marcelo	es_CL
Admission date	dc.date.accessioned	2007-05-18T15:18:10Z
Available date	dc.date.available	2007-05-18T15:18:10Z
Publication date	dc.date.issued	2005
Cita de ítem	dc.identifier.citation	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 357 (5): 1801-1828 2005	en
Identifier	dc.identifier.issn	0002-9947
Identifier	dc.identifier.uri	https://repositorio.uchile.cl/handle/2250/124601
Abstract	dc.description.abstract	We prove global existence of nonnegative solutions to the singular parabolic equation ut - Deltau+chi ({u> 0})(- u(-beta) +lambdaf(u)) = 0 in a smooth bounded domain Omega subset of R-N with zero Dirichlet boundary condition and initial condition u(0) is an element of C(Omega), u(0) greater than or equal to 0. In some cases we are also able to treat u(0) is an element of L-infinity(Omega). Then we show that if the stationary problem admits no solution which is positive a. e., then the solutions of the parabolic problem must vanish in finite time, a phenomenon called "quenching". We also establish a converse of this fact and study the solutions with a positive initial condition that leads to uniqueness on an appropriate class of functions.	en
Lenguage	dc.language.iso	en	en
Publisher	dc.publisher	AMER MATHEMATICAL SOC	en
Keywords	dc.subject	QUENCHING PROBLEMS	en
Título	dc.title	Existence and asymptotic behavior for a singular parabolic equation	en
Document type	dc.type	Artículo de revista