Blow-up rates for parabolic systems

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Abstract

Let Ω ⊂ ℝ n be a bounded domain andB R be a ball in ℝ n of radiusR. We consider two parabolic systems: utu +f(υ), υi=Δυ +g(u) in Ω × (0,T) withu=v=0 on δΩ × (0,T) andu t =Δu, v t =Δv inB r × (0,T) withδe/δv=f (v), δe/δv=g(u) onδB 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.