SOME TYPES OF REACTION-DIFFUSION SYSTEMS WITH NONLOCAL BOUNDARY CONDITIONS

Abstract

Abstract. This paper deals with some types of semilinear parabolic sys-tems with localized or nonlocal sources and nonlocal boundary conditions.The authors first derive some global existence and blow-up criteria. Andthen, for blow-up solutions, they study the global blow-up property aswell as the precise blow-up rate estimates, which has been seldom stud-ied until now. 1. IntroductionIn this paper, we investigate several types of reaction-diffusion systems withlocalized or nonlocal sources and nonlocal boundary conditions. We first studythe following two power-type systems with localized reaction terms(1.1) u t = ∆u+v p (x 0 ,t), v t = ∆v+u q (x 0 ,t), x∈ Ω, t>0,and with nonlocal sources(1.2) u t = ∆u+Z Ω v p (y,t)dy, v t = ∆v+Z Ω u q (y,t)dy, x∈ Ω, t>0,respectively, where Ω ⊂ R N (N≥ 1) is a bounded domain with smooth bound-ary ∂Ω, x 0 is a fixed point in Ω and p,q>0. And then, we investigate twoexponent-type systems with localized sources(1.3) u t = ∆u+λe pv(x 0 ,t) , v t = ∆v+µe