Analysis and numerical approximation of viscosity solutions with shocks

We consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. The new class of Hamilton-Jacobi equations represents the propagation of...

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Detalhes bibliográficos
Autor: Serna, Susana|||0000-0002-0908-4680
Tipo de documento: capítulo de livro
Data de publicação:2011
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:150400
Acesso em linha:https://ddd.uab.cat/record/150400
https://dx.doi.org/urn:doi:10.1063/1.3663455
Access Level:Acceso aberto
Palavra-chave:Fokker-Planck equation
Hamilton-Jacobi equations
Plasma equation
Numerical schemes
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spelling Analysis and numerical approximation of viscosity solutions with shocksapplication to the plasma equationSerna, Susana|||0000-0002-0908-4680Fokker-Planck equationHamilton-Jacobi equationsPlasma equationNumerical schemesWe consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. The new class of Hamilton-Jacobi equations represents the propagation of fronts with speed that is a nonlinear function of the signal. The equations contain a nonstandard Hamiltonian that allows the presence of shocks in the solution and these shocks propagate with nonlinear velocity. We focus on the one-dimensional plasma equation as an example of the general Fokker-Planck equations having the features we are interested in analyzing. We explore features of the solution of the corresponding Hamilton-Jacobi plasma equation and propose a suitable fifth order finite difference numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We present numerical results performed under different initial data with compact support. 22011-01-0120112011-01-01Capítol de llibrehttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://ddd.uab.cat/record/150400https://dx.doi.org/urn:doi:10.1063/1.3663455reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03597open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1504002026-06-06T12:50:31Z
dc.title.none.fl_str_mv Analysis and numerical approximation of viscosity solutions with shocks
application to the plasma equation
title Analysis and numerical approximation of viscosity solutions with shocks
spellingShingle Analysis and numerical approximation of viscosity solutions with shocks
Serna, Susana|||0000-0002-0908-4680
Fokker-Planck equation
Hamilton-Jacobi equations
Plasma equation
Numerical schemes
title_short Analysis and numerical approximation of viscosity solutions with shocks
title_full Analysis and numerical approximation of viscosity solutions with shocks
title_fullStr Analysis and numerical approximation of viscosity solutions with shocks
title_full_unstemmed Analysis and numerical approximation of viscosity solutions with shocks
title_sort Analysis and numerical approximation of viscosity solutions with shocks
dc.creator.none.fl_str_mv Serna, Susana|||0000-0002-0908-4680
author Serna, Susana|||0000-0002-0908-4680
author_facet Serna, Susana|||0000-0002-0908-4680
author_role author
dc.subject.none.fl_str_mv Fokker-Planck equation
Hamilton-Jacobi equations
Plasma equation
Numerical schemes
topic Fokker-Planck equation
Hamilton-Jacobi equations
Plasma equation
Numerical schemes
description We consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. The new class of Hamilton-Jacobi equations represents the propagation of fronts with speed that is a nonlinear function of the signal. The equations contain a nonstandard Hamiltonian that allows the presence of shocks in the solution and these shocks propagate with nonlinear velocity. We focus on the one-dimensional plasma equation as an example of the general Fokker-Planck equations having the features we are interested in analyzing. We explore features of the solution of the corresponding Hamilton-Jacobi plasma equation and propose a suitable fifth order finite difference numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We present numerical results performed under different initial data with compact support.
publishDate 2011
dc.date.none.fl_str_mv 2
2011-01-01
2011
2011-01-01
dc.type.none.fl_str_mv Capítol de llibre
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150400
https://dx.doi.org/urn:doi:10.1063/1.3663455
url https://ddd.uab.cat/record/150400
https://dx.doi.org/urn:doi:10.1063/1.3663455
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03597
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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