Blow-up rates for parabolic systems

Let ⁿ be a bounded domain andB_R be a ball in ⁿ of radiusR. We consider two parabolic systems: ut=u +f(), i= +g(u) in × (0,T) withu=v=0 on × (0,T) andu_t=u, v_t=v inB_r × (0,T) withe/v=f (v), e/v=g(u) onB_R × (0,T). Whenf(v) andg(u) are power law or exponential functions, we establish estimates on the blow-up rates for nonnegative solutions of the systems.