Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
We consider the equation Delta u = 0 posed in Q := (0;+infty)imes Omega, Omega:= { x=(x',x_N)/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0)u_{tt} + A(t,x',0)u_t - u_{x_N} geq D(t, x',0)|u|^q on Sigma := (0,+infty) imes R^{N-1} imes {0} and give c...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2004-01-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7475/4299 |
| _version_ | 1819230157431373824 |
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| author | Stanislav I. POHOZAEV Eric NABANA Mokhtar KIRANE |
| author_facet | Stanislav I. POHOZAEV Eric NABANA Mokhtar KIRANE |
| author_sort | Stanislav I. POHOZAEV |
| collection | DOAJ |
| description | We consider the equation Delta u = 0 posed in Q := (0;+infty)imes Omega, Omega:= { x=(x',x_N)/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0)u_{tt} + A(t,x',0)u_t - u_{x_N} geq D(t, x',0)|u|^q on Sigma := (0,+infty) imes R^{N-1} imes {0} and give conditions on the coefficient functions A(t,x',0); B(t,x',0) and D(t;x',0) for the nonexistence of global solutions. |
| first_indexed | 2024-12-23T11:24:36Z |
| format | Article |
| id | doaj.art-4faf7fab40e94b95861f7697318563d4 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-23T11:24:36Z |
| publishDate | 2004-01-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-4faf7fab40e94b95861f7697318563d42022-12-21T17:48:58ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882004-01-01222916Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary ConditionStanislav I. POHOZAEVEric NABANAMokhtar KIRANEWe consider the equation Delta u = 0 posed in Q := (0;+infty)imes Omega, Omega:= { x=(x',x_N)/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0)u_{tt} + A(t,x',0)u_t - u_{x_N} geq D(t, x',0)|u|^q on Sigma := (0,+infty) imes R^{N-1} imes {0} and give conditions on the coefficient functions A(t,x',0); B(t,x',0) and D(t;x',0) for the nonexistence of global solutions.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7475/4299non-existenceelliptic equationdynamical boundary condition. |
| spellingShingle | Stanislav I. POHOZAEV Eric NABANA Mokhtar KIRANE Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition Boletim da Sociedade Paranaense de Matemática non-existence elliptic equation dynamical boundary condition. |
| title | Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition |
| title_full | Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition |
| title_fullStr | Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition |
| title_full_unstemmed | Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition |
| title_short | Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition |
| title_sort | nonexistence of global solutions to an elliptic equation with a dynamical boundary condition |
| topic | non-existence elliptic equation dynamical boundary condition. |
| url | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7475/4299 |
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