Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model
This paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions. Under somepracticable regularity criteria on diffusion item and nonlinearity, weestablish the local existence and uniqu...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017025 |
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| author | Zijuan Wen Meng Fan Asim M. Asiri Ebraheem O. Alzahrani Mohamed M. El-Dessoky Yang Kuang |
| author_facet | Zijuan Wen Meng Fan Asim M. Asiri Ebraheem O. Alzahrani Mohamed M. El-Dessoky Yang Kuang |
| author_sort | Zijuan Wen |
| collection | DOAJ |
| description | This paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions. Under somepracticable regularity criteria on diffusion item and nonlinearity, weestablish the local existence and uniqueness of classical solutionsbased on a contraction mapping. This local solution can be continuedfor all positive time by employing the methods of energy estimates, $ L^{p} $-theory, and Schauder estimate of linear parabolic equations. Astraightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitroglioblastoma growth is also presented. |
| format | Article |
| id | doaj-art-8e8968929c724c5dbf6ff4dbf3a544d6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8e8968929c724c5dbf6ff4dbf3a544d62025-01-24T02:39:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-03-0114240742010.3934/mbe.2017025Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth modelZijuan Wen0Meng Fan1Asim M. Asiri2Ebraheem O. Alzahrani3Mohamed M. El-Dessoky4Yang Kuang5School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaSchool of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, ChinaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaSchool of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USAThis paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions. Under somepracticable regularity criteria on diffusion item and nonlinearity, weestablish the local existence and uniqueness of classical solutionsbased on a contraction mapping. This local solution can be continuedfor all positive time by employing the methods of energy estimates, $ L^{p} $-theory, and Schauder estimate of linear parabolic equations. Astraightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitroglioblastoma growth is also presented.https://www.aimspress.com/article/doi/10.3934/mbe.2017025quasilinear parabolic equationglioblastoma growth modelregularitycontraction mapdensity-dependent diffusion |
| spellingShingle | Zijuan Wen Meng Fan Asim M. Asiri Ebraheem O. Alzahrani Mohamed M. El-Dessoky Yang Kuang Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model Mathematical Biosciences and Engineering quasilinear parabolic equation glioblastoma growth model regularity contraction map density-dependent diffusion |
| title | Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| title_full | Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| title_fullStr | Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| title_full_unstemmed | Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| title_short | Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| title_sort | global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model |
| topic | quasilinear parabolic equation glioblastoma growth model regularity contraction map density-dependent diffusion |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017025 |
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