Blow-up phenomena for a class of nonlinear reaction-diffusion equations under nonlinear boundary conditions
Lingling Zhang, Huimin Tian · Applicable Analysis · 2018
The paper considers the blow-up solution for the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: (h(u))t=∇⋅(ρ(|∇u|p)|∇u|p−2∇u)+b(x)k(t)f(u),(x,t)∈Ω×(0,T),ρ(|∇u|p)|∇u|p−2∂u∂n=g(u),(x,t)∈∂Ω×(0,T),u(x,0)=u0(x)≥0,x∈Ω¯, where p>2 and Ω⊂RN(N>2) is a bounded convex domain with smooth boundary ∂Ω. By means of constructing auxiliary functions and a first-order differential inequality technique, we obtain the upper and lower bounds on blow-up time under some appropriate assumptions. Moreover, some examples are also presented as application of our main results.