Blow-up solutions for reaction diffusion equations with nonlocal boundary conditions

Abstract

We devote to investigating the following nonlinear reaction diffusion equations with nonlocal boundary conditions{ut=∇⋅(ρ(u)∇u)+k1(t)f(u)inD×(0,t⁎),∂u∂ν=k2(t)∫Dg(u)dxon∂D×(0,t⁎),u(x,0)=u0(x)≥0inD‾, where D is a bounded convex region in Rn(n≥2), and the boundary ∂D is smooth. By constructing some auxiliary functions and using differential inequality technique, we derive that the solution blows up at some finite time. Moreover, upper and lower bounds of the blow-up time are obtained.