Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approx...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2008-03-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/46/abstr.html |
| _version_ | 1818444790445899776 |
|---|---|
| author | Eleni Bisognin Vanilde Bisognin Ademir Fernando Pazoto Ruy Coimbra Charao |
| author_facet | Eleni Bisognin Vanilde Bisognin Ademir Fernando Pazoto Ruy Coimbra Charao |
| author_sort | Eleni Bisognin |
| collection | DOAJ |
| description | In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel. |
| first_indexed | 2024-12-14T19:21:32Z |
| format | Article |
| id | doaj.art-08855addbaaa4a3095066d71fcdeae6a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T19:21:32Z |
| publishDate | 2008-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-08855addbaaa4a3095066d71fcdeae6a2022-12-21T22:50:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912008-03-01200846123Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficientsEleni BisogninVanilde BisogninAdemir Fernando PazotoRuy Coimbra CharaoIn this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.http://ejde.math.txstate.edu/Volumes/2008/46/abstr.htmlAsymptotic behaviorhomogenizationpartial differential equationsmedia with periodic structuresecond-order hyperbolic equations |
| spellingShingle | Eleni Bisognin Vanilde Bisognin Ademir Fernando Pazoto Ruy Coimbra Charao Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients Electronic Journal of Differential Equations Asymptotic behavior homogenization partial differential equations media with periodic structure second-order hyperbolic equations |
| title | Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients |
| title_full | Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients |
| title_fullStr | Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients |
| title_full_unstemmed | Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients |
| title_short | Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients |
| title_sort | asymptotic behavior for a dissipative plate equation in r n with periodic coefficients |
| topic | Asymptotic behavior homogenization partial differential equations media with periodic structure second-order hyperbolic equations |
| url | http://ejde.math.txstate.edu/Volumes/2008/46/abstr.html |
| work_keys_str_mv | AT elenibisognin asymptoticbehaviorforadissipativeplateequationinrnwithperiodiccoefficients AT vanildebisognin asymptoticbehaviorforadissipativeplateequationinrnwithperiodiccoefficients AT ademirfernandopazoto asymptoticbehaviorforadissipativeplateequationinrnwithperiodiccoefficients AT ruycoimbracharao asymptoticbehaviorforadissipativeplateequationinrnwithperiodiccoefficients |