Asymptotic behaviour of solutions for porous medium equation with periodic absorption
This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may b...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201003581 |
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| _version_ | 1832555968479625216 |
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| author | Yin Jingxue Wang Yifu |
| author_facet | Yin Jingxue Wang Yifu |
| author_sort | Yin Jingxue |
| collection | DOAJ |
| description | This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is unstable. We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is stable. |
| format | Article |
| id | doaj-art-0a83de42e65d4a73815d3dfa219cdc0e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0a83de42e65d4a73815d3dfa219cdc0e2025-02-03T05:46:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01261354410.1155/S0161171201003581Asymptotic behaviour of solutions for porous medium equation with periodic absorptionYin Jingxue0Wang Yifu1Department of Mathematics, Jilin University, Changchun 130012, ChinaDepartment of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaThis paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is unstable. We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is stable.http://dx.doi.org/10.1155/S0161171201003581 |
| spellingShingle | Yin Jingxue Wang Yifu Asymptotic behaviour of solutions for porous medium equation with periodic absorption International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| title_full | Asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| title_fullStr | Asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| title_full_unstemmed | Asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| title_short | Asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| title_sort | asymptotic behaviour of solutions for porous medium equation with periodic absorption |
| url | http://dx.doi.org/10.1155/S0161171201003581 |
| work_keys_str_mv | AT yinjingxue asymptoticbehaviourofsolutionsforporousmediumequationwithperiodicabsorption AT wangyifu asymptoticbehaviourofsolutionsforporousmediumequationwithperiodicabsorption |