Optimal Sub- or Supersolutions in Reaction-Diffusion Problems

AbstractThe type of problem under consideration isut=Δu+f(u)inΩ×(0, T)∂u∂n+g(u)=0on∂Ω×(0, T) (*)u(x, 0)=u0(x). Here Ω is a finite domain of RN. The solution of (*) is compared with a corresponding solution of the N-ball or a finite interval whose size depends on different quantities of an associated linear elliptic problem for Ω, such as e.g. the fixed membrane problem. Possible applications include estimates for the blow-up or finite vanishing time