Global existence of the $\epsilon$-regular solution for the strongly damping wave equation
In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix $\mathbf{A}_{\theta}$, analysis the criticality of the $\varepsilon$-regular nonlinearity with critical...
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| Format: | Article |
| Language: | English |
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University of Szeged
2013-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2270 |
| _version_ | 1797830629361975296 |
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| author | Qinghua Zhang |
| author_facet | Qinghua Zhang |
| author_sort | Qinghua Zhang |
| collection | DOAJ |
| description | In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix $\mathbf{A}_{\theta}$, analysis the criticality of the $\varepsilon$-regular nonlinearity with critical growth. Finally, we investigate the global existence of the $\varepsilon$-regular solutions which have bounded $X^{1/2}\times X$ norms on their existence intervals. |
| first_indexed | 2024-04-09T13:39:09Z |
| format | Article |
| id | doaj.art-27405ea350e748c8a608c9610c59c824 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:09Z |
| publishDate | 2013-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-27405ea350e748c8a608c9610c59c8242023-05-09T07:53:03ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752013-11-0120136211110.14232/ejqtde.2013.1.622270Global existence of the $\epsilon$-regular solution for the strongly damping wave equationQinghua Zhang0School of Sciences, Nantong University, Nantong City 226019, P.R.ChinaIn this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix $\mathbf{A}_{\theta}$, analysis the criticality of the $\varepsilon$-regular nonlinearity with critical growth. Finally, we investigate the global existence of the $\varepsilon$-regular solutions which have bounded $X^{1/2}\times X$ norms on their existence intervals.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2270negative laplacian; wave equation; strong damping; sectorial operator; fractional power; interpolation and extrapolation spaces; criticality; $\varepsilon$-regular solution; global existence |
| spellingShingle | Qinghua Zhang Global existence of the $\epsilon$-regular solution for the strongly damping wave equation Electronic Journal of Qualitative Theory of Differential Equations negative laplacian; wave equation; strong damping; sectorial operator; fractional power; interpolation and extrapolation spaces; criticality; $\varepsilon$-regular solution; global existence |
| title | Global existence of the $\epsilon$-regular solution for the strongly damping wave equation |
| title_full | Global existence of the $\epsilon$-regular solution for the strongly damping wave equation |
| title_fullStr | Global existence of the $\epsilon$-regular solution for the strongly damping wave equation |
| title_full_unstemmed | Global existence of the $\epsilon$-regular solution for the strongly damping wave equation |
| title_short | Global existence of the $\epsilon$-regular solution for the strongly damping wave equation |
| title_sort | global existence of the epsilon regular solution for the strongly damping wave equation |
| topic | negative laplacian; wave equation; strong damping; sectorial operator; fractional power; interpolation and extrapolation spaces; criticality; $\varepsilon$-regular solution; global existence |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2270 |
| work_keys_str_mv | AT qinghuazhang globalexistenceoftheepsilonregularsolutionforthestronglydampingwaveequation |