Blow‐up analysis for a class of nonlinear reaction diffusion equations with Robin boundary conditions

This paper is devoted to the study of the blow‐up phenomena of following nonlinear reaction diffusion equations with Robin boundary conditions:g ( u )t = ∇ · ( ρ ( | ∇ u | 2 ) ∇ u ) + k ( t ) f ( u ) in Ω × ( 0 , t ∗ ) ,∂ u ∂ ν + γ u = 0 on ∂ Ω × ( 0 , t ∗ ) ,u ( x , 0 ) = u 0 ( x ) inΩ ¯ .Here, Ω ⊂ R n( n ⩾ 2 ) 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 u 0 . Moreover, we dedicate an upper bound and a lower bound for the blow‐up time when blowup occurs.