Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions
In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. Using the technique of a first-order differential inequality and the Sobolev inequalities, we can get the energy expression which satisfies t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7480676 |
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| _version_ | 1832566213444632576 |
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| author | Baiping Ouyang Wei Fan Yiwu Lin |
| author_facet | Baiping Ouyang Wei Fan Yiwu Lin |
| author_sort | Baiping Ouyang |
| collection | DOAJ |
| description | In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. Using the technique of a first-order differential inequality and the Sobolev inequalities, we can get the energy expression which satisfies the differential inequality. The lower bound for the blow-up time could be obtained if blow-up does really occur in high dimensions. |
| format | Article |
| id | doaj-art-6f8bcd3e23ef4b60a41d90915521cbaa |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6f8bcd3e23ef4b60a41d90915521cbaa2025-02-03T01:04:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/74806767480676Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High DimensionsBaiping Ouyang0Wei Fan1Yiwu Lin2College of Data Science, Huashang College Guangdong University of Finance & Economics, Guangzhou 511300, ChinaThe School of Gifted Young, University of Science and Technology of China, Hefei, ChinaDepartment of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, ChinaIn this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. Using the technique of a first-order differential inequality and the Sobolev inequalities, we can get the energy expression which satisfies the differential inequality. The lower bound for the blow-up time could be obtained if blow-up does really occur in high dimensions.http://dx.doi.org/10.1155/2020/7480676 |
| spellingShingle | Baiping Ouyang Wei Fan Yiwu Lin Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions Discrete Dynamics in Nature and Society |
| title | Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions |
| title_full | Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions |
| title_fullStr | Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions |
| title_full_unstemmed | Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions |
| title_short | Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions |
| title_sort | lower bound for the blow up time for the nonlinear reaction diffusion system in high dimensions |
| url | http://dx.doi.org/10.1155/2020/7480676 |
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