REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY
We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under certain extra assumptions (namely on the nonlinear term), we show the existence of a c...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2019-07-01
|
| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/148 |
| _version_ | 1818210621814996992 |
|---|---|
| author | Joseph L. Shomberg |
| author_facet | Joseph L. Shomberg |
| author_sort | Joseph L. Shomberg |
| collection | DOAJ |
| description | We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under certain extra assumptions (namely on the nonlinear term), we show the existence of a compact attracting set which provides further regularity for the global attractor and show that it consists of regular solutions. |
| first_indexed | 2024-12-12T05:19:31Z |
| format | Article |
| id | doaj.art-97f579f824f0425ba0edbf0fe0527c12 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-12T05:19:31Z |
| publishDate | 2019-07-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-97f579f824f0425ba0edbf0fe0527c122022-12-22T00:36:40ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522019-07-015110.15826/umj.2019.1.00776REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORYJoseph L. Shomberg0Department of Mathematics and Computer Science, Providence College, Providence, RI 02918We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under certain extra assumptions (namely on the nonlinear term), we show the existence of a compact attracting set which provides further regularity for the global attractor and show that it consists of regular solutions.https://umjuran.ru/index.php/umj/article/view/148Degenerate viscoelasticity, Relative displacement history, Nonlinear wave equation, Critical exponent, Regular global attractor |
| spellingShingle | Joseph L. Shomberg REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY Ural Mathematical Journal Degenerate viscoelasticity, Relative displacement history, Nonlinear wave equation, Critical exponent, Regular global attractor |
| title | REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY |
| title_full | REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY |
| title_fullStr | REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY |
| title_full_unstemmed | REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY |
| title_short | REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY |
| title_sort | regular global attractors for wave equations with degenerate memory |
| topic | Degenerate viscoelasticity, Relative displacement history, Nonlinear wave equation, Critical exponent, Regular global attractor |
| url | https://umjuran.ru/index.php/umj/article/view/148 |
| work_keys_str_mv | AT josephlshomberg regularglobalattractorsforwaveequationswithdegeneratememory |