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.
