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Blow-up rates for parabolic systems

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Abstract

Let Ω ⊂ ℝn be a bounded domain andB R be a ball in ℝn of radiusR. We consider two parabolic systems: ut=Δu +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.

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  1. Department of Mathematics, University of Southwestern Louisiana, 70504, Lafayette, Louisiana, USA

    Keng Deng

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  1. Keng Deng
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Deng, K. Blow-up rates for parabolic systems. Z. angew. Math. Phys. 47, 132–143 (1996). https://doi.org/10.1007/BF00917578

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  • DOI: https://doi.org/10.1007/BF00917578

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