Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions
In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensu...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-12-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0088/math-2020-0088.xml?format=INT |
| _version_ | 1818339275432787968 |
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| author | Tian Huimin Zhang Lingling |
| author_facet | Tian Huimin Zhang Lingling |
| author_sort | Tian Huimin |
| collection | DOAJ |
| description | In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u(x,t)u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results. |
| first_indexed | 2024-12-13T15:24:25Z |
| format | Article |
| id | doaj.art-5f92aa1e09e242279919b197dfab3607 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T15:24:25Z |
| publishDate | 2020-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-5f92aa1e09e242279919b197dfab36072022-12-21T23:40:25ZengDe GruyterOpen Mathematics2391-54552020-12-011811552156410.1515/math-2020-0088math-2020-0088Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditionsTian Huimin0Zhang Lingling1College of Mathematics, Taiyuan University of Technology, Taiyuan, ChinaCollege of Mathematics, Taiyuan University of Technology, Taiyuan, ChinaIn this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u(x,t)u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0088/math-2020-0088.xml?format=INTreaction diffusion equationsblow uplower and upper bounds35b4435k5735k5135a01 |
| spellingShingle | Tian Huimin Zhang Lingling Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions Open Mathematics reaction diffusion equations blow up lower and upper bounds 35b44 35k57 35k51 35a01 |
| title | Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions |
| title_full | Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions |
| title_fullStr | Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions |
| title_full_unstemmed | Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions |
| title_short | Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions |
| title_sort | blow up analyses in nonlocal reaction diffusion equations with time dependent coefficients under neumann boundary conditions |
| topic | reaction diffusion equations blow up lower and upper bounds 35b44 35k57 35k51 35a01 |
| url | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0088/math-2020-0088.xml?format=INT |
| work_keys_str_mv | AT tianhuimin blowupanalysesinnonlocalreactiondiffusionequationswithtimedependentcoefficientsunderneumannboundaryconditions AT zhanglingling blowupanalysesinnonlocalreactiondiffusionequationswithtimedependentcoefficientsunderneumannboundaryconditions |