Spatial dynamics for a model of epidermal wound healing
In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing.We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speedof a family of non-constant traveling wave solu...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1215 |
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| author | Haiyan Wang Shiliang Wu |
| author_facet | Haiyan Wang Shiliang Wu |
| author_sort | Haiyan Wang |
| collection | DOAJ |
| description | In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing.We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speedof a family of non-constant traveling wave solutions. We also construct some new types of entire solutions which are different from the traveling wave solutions and spatial variable independent solutions. The traveling wave solutions provide the healing speed and describe how wound healing process spreads from one side of the wound. The entire solution exhibits the interaction of several waves originated from different locations of the wound. To the best of knowledge of the authors, it is the first time that it is shown that there is an entire solution in the model for epidermal wound healing. |
| format | Article |
| id | doaj-art-c57d1ad3d82c456b90322d2d62e71b9a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c57d1ad3d82c456b90322d2d62e71b9a2025-01-24T02:28:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-05-011151215122710.3934/mbe.2014.11.1215Spatial dynamics for a model of epidermal wound healingHaiyan Wang0Shiliang Wu1Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi 710071In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing.We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speedof a family of non-constant traveling wave solutions. We also construct some new types of entire solutions which are different from the traveling wave solutions and spatial variable independent solutions. The traveling wave solutions provide the healing speed and describe how wound healing process spreads from one side of the wound. The entire solution exhibits the interaction of several waves originated from different locations of the wound. To the best of knowledge of the authors, it is the first time that it is shown that there is an entire solution in the model for epidermal wound healing.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1215non-cooperative diffusion systemsepidermal wound healing.entire solutiontraveling wavesspreading speed |
| spellingShingle | Haiyan Wang Shiliang Wu Spatial dynamics for a model of epidermal wound healing Mathematical Biosciences and Engineering non-cooperative diffusion systems epidermal wound healing. entire solution traveling waves spreading speed |
| title | Spatial dynamics for a model of epidermal wound healing |
| title_full | Spatial dynamics for a model of epidermal wound healing |
| title_fullStr | Spatial dynamics for a model of epidermal wound healing |
| title_full_unstemmed | Spatial dynamics for a model of epidermal wound healing |
| title_short | Spatial dynamics for a model of epidermal wound healing |
| title_sort | spatial dynamics for a model of epidermal wound healing |
| topic | non-cooperative diffusion systems epidermal wound healing. entire solution traveling waves spreading speed |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1215 |
| work_keys_str_mv | AT haiyanwang spatialdynamicsforamodelofepidermalwoundhealing AT shiliangwu spatialdynamicsforamodelofepidermalwoundhealing |