具奇异系数的反应扩散方程组Cauchy问题

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Abstract:

This paper is concerned with the local existence and nonexistence of nonneg ative solutions and blow up problem in a finite time for the reaction diffusion system with singular coefficients (u_t-t^{-1}Δ u=α_1u^{q_1}+β_1v^\{p_1}+f_1(x),t>0,x∈R^N； v_t-t^\{-1}Δ v=α_2u^\{q_2}+β_2v^{p_2}+f_2(x),t>0,x∈R^ N；lim_{t→0+}u(t,x)=lim_{t→0+}v(t,x)=0,x∈R^N. where p_i>1, q_i>1 (i=1, 2) , α_1≥0, α_2>0, β_1>0, β_2≥0, f_ i(x) (i=1, 2) are continuous, nonnegative and bounded functions, (f_1(x), f_2(x))(0, 0) .The authors give an explicit condition for the local existence of nonnegative solutions and a comparison result for the local nonexistence of nonnegative solutions of the system. Some blow up results for the system are also obtained.
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Key words: Reactiondiffusion system, Singular coefficient, Lo cal solution,Blow up

CLC Number:

35K55

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BANG Da-Heng, HAN Mao-An, WANG Zhi-Cheng. On the Cauchy Problem for a Reaction Diffusion System with Singular Coefficients[J].Acta mathematica scientia,Series A, 2005, 25(2): 220-229.

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On the Cauchy Problem for a Reaction Diffusion System with Singular Coefficients

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