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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Bibliographic Details
Published in:Discrete dynamics in nature and society 2022, Vol.2022 (1)
Main Authors: Shen, Xuhui, Wu, Dandan
Format: Article
Language:English
Subjects:
Inequality
Lower bounds
Smooth boundaries
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2022/8364982