文章基本信息

标题：Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms
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作者：Xuhui Shen ; Dandan Wu
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2022
卷号：2022
DOI：10.1155/2022/8364982
语种：English
出版社：Hindawi Publishing Corporation
摘要：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.