Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms
This paper considers the blow-up phenomena for the following reaction-diffusion problem with nonlocal and gradient terms: ut=Δum+∫Ωurdx−∇us,in Ω×0,t∗,∂u/∂ν=gu,on ∂Ω ×0,t∗,ux,0=u0x≥0,in Ω¯. Here m>1, and Ω⊂ℝNN≥2 is a bounded and convex domain with smooth boundary. Applying a Sobolev inequality a...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/8364982 |
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| _version_ | 1849306025609396224 |
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| author | Xuhui Shen Dandan Wu |
| author_facet | Xuhui Shen Dandan Wu |
| author_sort | Xuhui Shen |
| collection | DOAJ |
| description | This paper considers the blow-up phenomena for the following reaction-diffusion problem with nonlocal and gradient terms: ut=Δum+∫Ωurdx−∇us,in Ω×0,t∗,∂u/∂ν=gu,on ∂Ω ×0,t∗,ux,0=u0x≥0,in Ω¯. Here m>1, and Ω⊂ℝNN≥2 is a bounded and convex domain with smooth boundary. Applying a Sobolev inequality and a differential inequality technique, lower bounds for blow-up time when blow-up occurs are given. Moreover, two examples are given as applications to illustrate the abstract results obtained in this paper. |
| format | Article |
| id | doaj-art-3112c4e7226745408957fe61ac9dcde3 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3112c4e7226745408957fe61ac9dcde32025-08-20T03:55:12ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/8364982Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient TermsXuhui Shen0Dandan Wu1School of Applied MathematicsDepartment of Enterprise Information China Telecom Stocks Co., LtdThis paper considers the blow-up phenomena for the following reaction-diffusion problem with nonlocal and gradient terms: ut=Δum+∫Ωurdx−∇us,in Ω×0,t∗,∂u/∂ν=gu,on ∂Ω ×0,t∗,ux,0=u0x≥0,in Ω¯. Here m>1, and Ω⊂ℝNN≥2 is a bounded and convex domain with smooth boundary. Applying a Sobolev inequality and a differential inequality technique, lower bounds for blow-up time when blow-up occurs are given. Moreover, two examples are given as applications to illustrate the abstract results obtained in this paper.http://dx.doi.org/10.1155/2022/8364982 |
| spellingShingle | Xuhui Shen Dandan Wu Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms Discrete Dynamics in Nature and Society |
| title | Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms |
| title_full | Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms |
| title_fullStr | Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms |
| title_full_unstemmed | Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms |
| title_short | Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms |
| title_sort | blow up phenomena in reaction diffusion problems with nonlocal and gradient terms |
| url | http://dx.doi.org/10.1155/2022/8364982 |
| work_keys_str_mv | AT xuhuishen blowupphenomenainreactiondiffusionproblemswithnonlocalandgradientterms AT dandanwu blowupphenomenainreactiondiffusionproblemswithnonlocalandgradientterms |