Blow-up properties for parabolic systems with localized nonlinear source

摘要

This paper deals with blow-up properties of solutions to a semilinear parabolic system with nonlinear localized source involved a product with local terms u t = Δ u + exp{mu(x,t)+nv(x 0 ,t)}, v t = Δ v + exp{pu(x 0 ,t)+qv(x,t)} with homogeneous Dirichlet boundary conditions. We investigate the in.uence of localized sources and local terms on blow-up properties for this system, and prove that: (i)when m, q 0 this system possesses uniform blow-up profiles, in other words, the localized terms play a leading role in the blow-up profile for this case; (ii)when m, q > 0 , this system presents single point blow-up patterns, or say that local terms dominate localized terms in the blow-up profile. Moreover, the blow-up rate estimates in time and space are obtained, respectively.