Decay rates for solutions of semilinear wave equations with a memory condition at the boundary
In this paper, we study the stability of solutions for semilinear wave equations whoseboundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exp...
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| Format: | Article |
| Language: | English |
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University of Szeged
2002-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=108 |
| _version_ | 1827951448156012544 |
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| author | M. L. Santos |
| author_facet | M. L. Santos |
| author_sort | M. L. Santos |
| collection | DOAJ |
| description | In this paper, we study the stability of solutions for semilinear wave equations whoseboundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polinomially, we show that the solution decays polynomially and with the same rate. |
| first_indexed | 2024-04-09T13:43:01Z |
| format | Article |
| id | doaj.art-bc3df8e5d49b4ce58831865d41a7718b |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:43:01Z |
| publishDate | 2002-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-bc3df8e5d49b4ce58831865d41a7718b2023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752002-01-012002711710.14232/ejqtde.2002.1.7108Decay rates for solutions of semilinear wave equations with a memory condition at the boundaryM. L. Santos0UFPA, Para, BrazilIn this paper, we study the stability of solutions for semilinear wave equations whoseboundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polinomially, we show that the solution decays polynomially and with the same rate.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=108 |
| spellingShingle | M. L. Santos Decay rates for solutions of semilinear wave equations with a memory condition at the boundary Electronic Journal of Qualitative Theory of Differential Equations |
| title | Decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| title_full | Decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| title_fullStr | Decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| title_full_unstemmed | Decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| title_short | Decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| title_sort | decay rates for solutions of semilinear wave equations with a memory condition at the boundary |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=108 |
| work_keys_str_mv | AT mlsantos decayratesforsolutionsofsemilinearwaveequationswithamemoryconditionattheboundary |