On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000200002 |
Resumo: | In this paper, we study the nonlinear equation of the form <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent02.gif"> where is <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex03.gif" align=absmiddle>the ultra-hyperbolic operator iterated k-times, defined by <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent03.gif" align=absmiddle>, p + q = n is the dimension of the Euclidean space <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n, (x, t) = (x1, x2,..., xn, t) <img border=0 src="../../../../../../img/revistas/cam/v28n2/a01ent09.gif" align=absmiddle><img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n× (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">), k is a positive integer and c is a positive constant. On the suitable conditions for f , u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n × (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30. |
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Computational & Applied Mathematics |
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On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrumultra-hyperbolic heat equationthe Dirac delta distributionthe spectrumFourier transformIn this paper, we study the nonlinear equation of the form <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent02.gif"> where is <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex03.gif" align=absmiddle>the ultra-hyperbolic operator iterated k-times, defined by <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent03.gif" align=absmiddle>, p + q = n is the dimension of the Euclidean space <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n, (x, t) = (x1, x2,..., xn, t) <img border=0 src="../../../../../../img/revistas/cam/v28n2/a01ent09.gif" align=absmiddle><img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n× (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">), k is a positive integer and c is a positive constant. On the suitable conditions for f , u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n × (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30.Sociedade Brasileira de Matemática Aplicada e Computacional2009-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000200002Computational & Applied Mathematics v.28 n.2 2009reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022009000200002info:eu-repo/semantics/openAccessKananthai,AmnuayNonlaopon,Kamsingeng2009-07-14T00:00:00Zoai:scielo:S1807-03022009000200002Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2009-07-14T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
title |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
spellingShingle |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum Kananthai,Amnuay ultra-hyperbolic heat equation the Dirac delta distribution the spectrum Fourier transform |
title_short |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
title_full |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
title_fullStr |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
title_full_unstemmed |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
title_sort |
On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum |
author |
Kananthai,Amnuay |
author_facet |
Kananthai,Amnuay Nonlaopon,Kamsing |
author_role |
author |
author2 |
Nonlaopon,Kamsing |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Kananthai,Amnuay Nonlaopon,Kamsing |
dc.subject.por.fl_str_mv |
ultra-hyperbolic heat equation the Dirac delta distribution the spectrum Fourier transform |
topic |
ultra-hyperbolic heat equation the Dirac delta distribution the spectrum Fourier transform |
description |
In this paper, we study the nonlinear equation of the form <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent02.gif"> where is <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex03.gif" align=absmiddle>the ultra-hyperbolic operator iterated k-times, defined by <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent03.gif" align=absmiddle>, p + q = n is the dimension of the Euclidean space <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n, (x, t) = (x1, x2,..., xn, t) <img border=0 src="../../../../../../img/revistas/cam/v28n2/a01ent09.gif" align=absmiddle><img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n× (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">), k is a positive integer and c is a positive constant. On the suitable conditions for f , u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n × (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000200002 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000200002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022009000200002 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
Computational & Applied Mathematics v.28 n.2 2009 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
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1754734890183557120 |