摘要
研究下列反应扩散方程组的 Cauchy问题ut-aΔu =-uψ( v) , ( x,t)∈ RN × ( 0 ,T],vt-cΔu -dΔv =uψ( v) , ( x,t)∈ RN× ( 0 ,T],u( x,0 ) =u0 ( x) , v( x,0 ) =v0 ( x) , x∈ RN .利用迭代法证明此 Cauchy问题整体古典解的存在性和惟一性 .同时指出若在 RN上 u0 ( x)≥ 0 ,v0 ( x)≥ 0 ,则在RN × [0 ,T]上 u( x,t)≥ 0 ,v( x,t)≥ 0 .
The following Cauchy problem for a system of reaction-diffusion equation u t-aΔu=-uψ(v), (x,t)∈RN×(0,T], , v t-cΔu-dΔv=uψ(v), (x,t)∈RN×(0,T], , u(x,0)=u 0(x), v(x,0)=v 0(x), x∈RNis studied. This existence and uniqueness of global classical solution of the Cauchy problem are proved by the iterative method. Moreover, this result shows that if u 0(x)≥0, v 0(x)≥0 in RN, then u(x,t)≥0, v(x,t)≥0 in RN×.
出处
《郑州大学学报（自然科学版）》
2001年第3期5-12,共8页
Journal of Zhengzhou University (Natural Science)
基金
Supported by National Natural Science Foundation of China( No.10 0 710 74) and by Natural Science Foundation ofHenan Province
