This paper is devoted to the study of the blow‐up phenomena of following nonlinear reaction diffusion equations with Robin boundary conditions:
()gfalse(ufalse)t=∇·false(ρfalse(false|∇u|2false)∇ufalse)+kfalse(tfalse)ffalse(ufalse)in.5emnormalΩ×false(0,t∗false),∂u∂ν+γu=0on.5em∂normalΩ×false(0,t∗false),ufalse(x,0false)=u0false(xfalse)in.5emtrueΩ¯.
Here,
normalΩ⊂Rn.5emfalse(n⩾2false) is a bounded convex domain with smooth boundary. With the aid of a differential inequality technique and maximum principles, we establish a blow‐up or non–blow‐up criterion under some appropriate assumptions on the functions f,g,ρ,k, and u0. Moreover, we dedicate an upper bound and a lower bound for the blow‐up time when blowup occurs.
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