A nonlocal diffusion equation whose solutions develop a free boundary

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dc.contributor.authorCortazar, C
dc.contributor.authorElgueta, M
dc.contributor.authorRossi, JD
dc.date.accessioned2025-01-21T01:07:03Z
dc.date.available2025-01-21T01:07:03Z
dc.date.issued2005
dc.description.abstractLet J : R -> R be a nonnegative, smooth compactly supported function such that integral(R) J(r)dr = 1. We consider the nonlocal diffusion problem
dc.description.abstractut(x, t) = integral(R) J (x - y/u(y,t)) dy - u(x,t) in R x [0, infinity)
dc.description.abstractwith a nonnegative initial condition. Under suitable hypotheses we prove existence, uniqueness, as well as the validity of a comparison principle for solutions of this problem. Moreover we show that if u(., 0) is bounded and compactly supported, then u(., t) is compactly supported for all positive times t. This implies the existence of a free boundary, analog to the corresponding one for the porous media equation, for this model.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00023-005-0206-z
dc.identifier.issn1424-0637
dc.identifier.urihttps://doi.org/10.1007/s00023-005-0206-z
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/96268
dc.identifier.wosidWOS:000228868300004
dc.issue.numero2
dc.language.isoen
dc.pagina.final281
dc.pagina.inicio269
dc.revistaAnnales henri poincare
dc.rightsacceso restringido
dc.subject.ods03 Good Health and Well-being
dc.subject.odspa03 Salud y bienestar
dc.titleA nonlocal diffusion equation whose solutions develop a free boundary
dc.typeartículo
dc.volumen6
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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