Front propagation in Fisher-KPP equations with fractional diffusion

We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable...

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Authors: Cabré Vilagut, Xavier|||0000-0001-5682-3135, Roquejoffre, Jean-Michel
Format: report
Publication Date:2009
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/11076
Online Access:https://hdl.handle.net/2117/11076
Access Level:Open access
Keyword:Differential equations
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Front propagation in Fisher-KPP equations with fractional diffusionCabré Vilagut, Xavier|||0000-0001-5682-3135Roquejoffre, Jean-MichelDifferential equationsEquacions diferencialsÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable one at constant speed, we prove here that invasion holds at an exponential in time velocity. These results provide a mathematically rigorous justification of numerous heuristics about this model.20092009-05-0120112011-01-18reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/11076reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/110762026-05-27T15:37:01Z
dc.title.none.fl_str_mv Front propagation in Fisher-KPP equations with fractional diffusion
title Front propagation in Fisher-KPP equations with fractional diffusion
spellingShingle Front propagation in Fisher-KPP equations with fractional diffusion
Cabré Vilagut, Xavier|||0000-0001-5682-3135
Differential equations
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Front propagation in Fisher-KPP equations with fractional diffusion
title_full Front propagation in Fisher-KPP equations with fractional diffusion
title_fullStr Front propagation in Fisher-KPP equations with fractional diffusion
title_full_unstemmed Front propagation in Fisher-KPP equations with fractional diffusion
title_sort Front propagation in Fisher-KPP equations with fractional diffusion
dc.creator.none.fl_str_mv Cabré Vilagut, Xavier|||0000-0001-5682-3135
Roquejoffre, Jean-Michel
author Cabré Vilagut, Xavier|||0000-0001-5682-3135
author_facet Cabré Vilagut, Xavier|||0000-0001-5682-3135
Roquejoffre, Jean-Michel
author_role author
author2 Roquejoffre, Jean-Michel
author2_role author
dc.subject.none.fl_str_mv Differential equations
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Differential equations
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable one at constant speed, we prove here that invasion holds at an exponential in time velocity. These results provide a mathematically rigorous justification of numerous heuristics about this model.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-05-01
2011
2011-01-18
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/11076
url https://hdl.handle.net/2117/11076
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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