Publicação
Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation
| Resumo: | We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5]. |
|---|---|
| Autores principais: | Panthee, Mahendra |
| Outros Autores: | Scialom, Marcia |
| Assunto: | Dispersive equation KdV equation Blow-up solution |
| Ano: | 2010 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1877776581572689920 |
|---|---|
| author | Panthee, Mahendra |
| author2 | Scialom, Marcia |
| author2_role | author |
| author_facet | Panthee, Mahendra Scialom, Marcia |
| author_role | author |
| contributor_name_str_mv | RepositóriUM - Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Panthee, Mahendra\"},{\"Person.name\":\"Scialom, Marcia\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | RepositóriUM - Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Panthee, Mahendra Scialom, Marcia |
| datacite.date.Accepted.fl_str_mv | 2010-01-01T00:00:00Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Dispersive equation KdV equation Blow-up solution |
| datacite.titles.title.fl_str_mv | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| dc.contributor.none.fl_str_mv | RepositóriUM - Universidade do Minho |
| dc.creator.none.fl_str_mv | Panthee, Mahendra Scialom, Marcia |
| dc.date.Accepted.fl_str_mv | 2010-01-01T00:00:00Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/11581 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Wiley |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Dispersive equation KdV equation Blow-up solution |
| dc.title.fl_str_mv | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5]. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | rum_4b0b6cdb102e77655d9a1e7e636c8aba |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/11581 |
| inst_facet_str | urn:organizationAcronym:repositorium{{{_:::_}}}Universidade do Minho |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/11581 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Panthee, Mahendra Scialom, Marcia |
| publishDate | 2010 |
| publisher.none.fl_str_mv | Wiley |
| repo_facet_str | urn:repositoryAcronym:rum{{{_:::_}}}RepositóriUM - Universidade do Minho |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engWileyporWe consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5].application/pdfporAsymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equationPanthee, MahendraScialom, MarciaHostingInstitutionOrganizationalRepositóriUM - Universidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptCITATION"Studies in Applied Mathematics". ISSN 1467-9590. 124:3 (2010) 229-245.ISSNIsPartOf1467-9590DOIIsPartOf10.1111/j.1467-9590.2009.00469.x20102010-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/11581http://purl.org/coar/access_right/c_abf2open accessDispersive equationKdV equationBlow-up solution273557 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdfhttps://repositorium.uminho.pt/bitstreams/d6cfc5c2-498e-4d24-945e-e33e192d9119/download |
| spellingShingle | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation Panthee, Mahendra Dispersive equation KdV equation Blow-up solution |
| status | SINGLETON |
| subject.fl_str_mv | Dispersive equation KdV equation Blow-up solution |
| title | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| title_full | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| title_fullStr | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| title_full_unstemmed | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| title_short | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| title_sort | Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation |
| topic | Dispersive equation KdV equation Blow-up solution |
| topic_facet | Dispersive equation KdV equation Blow-up solution |
| url | https://hdl.handle.net/1822/11581 |
| visible | 1 |
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