Blow up of the Solutions of Nonlinear Wave Equation
<p/> <p>We construct for every fixed <inline-formula><graphic file="1687-2770-2007-042954-i1.gif"/></inline-formula> the metric <inline-formula><graphic file="1687-2770-2007-042954-i2.gif"/></inline-formula>, where <inline-formul...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2007/042954 |
| _version_ | 1818369282405302272 |
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| author | Georgiev Svetlin Georgiev |
| author_facet | Georgiev Svetlin Georgiev |
| author_sort | Georgiev Svetlin Georgiev |
| collection | DOAJ |
| description | <p/> <p>We construct for every fixed <inline-formula><graphic file="1687-2770-2007-042954-i1.gif"/></inline-formula> the metric <inline-formula><graphic file="1687-2770-2007-042954-i2.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i6.gif"/></inline-formula>, are continuous functions, <inline-formula><graphic file="1687-2770-2007-042954-i7.gif"/></inline-formula>, for which we consider the Cauchy problem <inline-formula><graphic file="1687-2770-2007-042954-i8.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i9.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i10.gif"/></inline-formula>; <inline-formula><graphic file="1687-2770-2007-042954-i11.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i12.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i13.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i14.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i15.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i16.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i17.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i18.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i19.gif"/></inline-formula> and <inline-formula><graphic file="1687-2770-2007-042954-i20.gif"/></inline-formula> are positive constants. When <inline-formula><graphic file="1687-2770-2007-042954-i21.gif"/></inline-formula>, we prove that the above Cauchy problem has a nontrivial solution <inline-formula><graphic file="1687-2770-2007-042954-i22.gif"/></inline-formula> in the form <inline-formula><graphic file="1687-2770-2007-042954-i23.gif"/></inline-formula> for which <inline-formula><graphic file="1687-2770-2007-042954-i24.gif"/></inline-formula>. When <inline-formula><graphic file="1687-2770-2007-042954-i25.gif"/></inline-formula>, we prove that the above Cauchy problem has a nontrivial solution <inline-formula><graphic file="1687-2770-2007-042954-i26.gif"/></inline-formula> in the form <inline-formula><graphic file="1687-2770-2007-042954-i27.gif"/></inline-formula> for which <inline-formula><graphic file="1687-2770-2007-042954-i28.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-13T23:21:22Z |
| format | Article |
| id | doaj.art-a21f8b4fd8b04deb9ef41be86a7b20a7 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T23:21:22Z |
| publishDate | 2007-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-a21f8b4fd8b04deb9ef41be86a7b20a72022-12-21T23:27:44ZengSpringerOpenBoundary Value Problems1687-27621687-27702007-01-0120071042954Blow up of the Solutions of Nonlinear Wave EquationGeorgiev Svetlin Georgiev<p/> <p>We construct for every fixed <inline-formula><graphic file="1687-2770-2007-042954-i1.gif"/></inline-formula> the metric <inline-formula><graphic file="1687-2770-2007-042954-i2.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i6.gif"/></inline-formula>, are continuous functions, <inline-formula><graphic file="1687-2770-2007-042954-i7.gif"/></inline-formula>, for which we consider the Cauchy problem <inline-formula><graphic file="1687-2770-2007-042954-i8.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i9.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i10.gif"/></inline-formula>; <inline-formula><graphic file="1687-2770-2007-042954-i11.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i12.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2007-042954-i13.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i14.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i15.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i16.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i17.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i18.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2007-042954-i19.gif"/></inline-formula> and <inline-formula><graphic file="1687-2770-2007-042954-i20.gif"/></inline-formula> are positive constants. When <inline-formula><graphic file="1687-2770-2007-042954-i21.gif"/></inline-formula>, we prove that the above Cauchy problem has a nontrivial solution <inline-formula><graphic file="1687-2770-2007-042954-i22.gif"/></inline-formula> in the form <inline-formula><graphic file="1687-2770-2007-042954-i23.gif"/></inline-formula> for which <inline-formula><graphic file="1687-2770-2007-042954-i24.gif"/></inline-formula>. When <inline-formula><graphic file="1687-2770-2007-042954-i25.gif"/></inline-formula>, we prove that the above Cauchy problem has a nontrivial solution <inline-formula><graphic file="1687-2770-2007-042954-i26.gif"/></inline-formula> in the form <inline-formula><graphic file="1687-2770-2007-042954-i27.gif"/></inline-formula> for which <inline-formula><graphic file="1687-2770-2007-042954-i28.gif"/></inline-formula>.</p>http://www.boundaryvalueproblems.com/content/2007/042954 |
| spellingShingle | Georgiev Svetlin Georgiev Blow up of the Solutions of Nonlinear Wave Equation Boundary Value Problems |
| title | Blow up of the Solutions of Nonlinear Wave Equation |
| title_full | Blow up of the Solutions of Nonlinear Wave Equation |
| title_fullStr | Blow up of the Solutions of Nonlinear Wave Equation |
| title_full_unstemmed | Blow up of the Solutions of Nonlinear Wave Equation |
| title_short | Blow up of the Solutions of Nonlinear Wave Equation |
| title_sort | blow up of the solutions of nonlinear wave equation |
| url | http://www.boundaryvalueproblems.com/content/2007/042954 |
| work_keys_str_mv | AT georgievsvetlingeorgiev blowupofthesolutionsofnonlinearwaveequation |