Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena
In this paper we consider a drying and wetting process in porous medium to create a mathematical model for concrete carbonation. The process is assumed to be characterized by the growth of the air zone and a diffusion of moisture in the air zone. Under the assumption we proposed a one-dimensional fr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2018-09-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | http://mathizv.isu.ru/assets/articles/afd320b2-8e86-4f34-817a-af0844a9586f.pdf |
| _version_ | 1818234216908849152 |
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| author | T. Aiki N. Sato |
| author_facet | T. Aiki N. Sato |
| author_sort | T. Aiki |
| collection | DOAJ |
| description | In this paper we consider a drying and wetting process in porous medium to create a mathematical model for concrete carbonation. The process is assumed to be characterized by the growth of the air zone and a diffusion of moisture in the air zone. Under the assumption we proposed a one-dimensional free boundary problem describing adsorption phenomena in a porous medium. The free boundary problem it to find a curve representing the air zone and the relative humidity of the air zone. For the problem we also established existence, uniqueness and a large time behavior of solutions. Here, by improving the method for uniform estimates we can show the existence of a periodic solution of the problem. Also, the extension method is applied in the proof. This idea is quite important and new since the value of the humidity on the free boundary is unknown. |
| first_indexed | 2024-12-12T11:34:33Z |
| format | Article |
| id | doaj.art-8e55de97889349c9bb0c75cef76e7ec3 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-12-12T11:34:33Z |
| publishDate | 2018-09-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-8e55de97889349c9bb0c75cef76e7ec32022-12-22T00:25:42ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852018-09-01251318https://doi.org/10.26516/1997-7670.2018.25.3Existence of periodic solution to one dimensional free boundary problems for adsorption phenomenaT. AikiN. SatoIn this paper we consider a drying and wetting process in porous medium to create a mathematical model for concrete carbonation. The process is assumed to be characterized by the growth of the air zone and a diffusion of moisture in the air zone. Under the assumption we proposed a one-dimensional free boundary problem describing adsorption phenomena in a porous medium. The free boundary problem it to find a curve representing the air zone and the relative humidity of the air zone. For the problem we also established existence, uniqueness and a large time behavior of solutions. Here, by improving the method for uniform estimates we can show the existence of a periodic solution of the problem. Also, the extension method is applied in the proof. This idea is quite important and new since the value of the humidity on the free boundary is unknown.http://mathizv.isu.ru/assets/articles/afd320b2-8e86-4f34-817a-af0844a9586f.pdffree boundary problemperiodic solutionfixed point argument |
| spellingShingle | T. Aiki N. Sato Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena Известия Иркутского государственного университета: Серия "Математика" free boundary problem periodic solution fixed point argument |
| title | Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| title_full | Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| title_fullStr | Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| title_full_unstemmed | Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| title_short | Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| title_sort | existence of periodic solution to one dimensional free boundary problems for adsorption phenomena |
| topic | free boundary problem periodic solution fixed point argument |
| url | http://mathizv.isu.ru/assets/articles/afd320b2-8e86-4f34-817a-af0844a9586f.pdf |
| work_keys_str_mv | AT taiki existenceofperiodicsolutiontoonedimensionalfreeboundaryproblemsforadsorptionphenomena AT nsato existenceofperiodicsolutiontoonedimensionalfreeboundaryproblemsforadsorptionphenomena |