It is shown that any solution to the semilinear problem{u（x,0=）u0（x）〈1,x∈[-1,1] u（±1,t）=0,t∈（0,T）, ut=uxx＋δ（1-u）^-p（x,t）∈（-1,1） ×（0,T）either touches 1 in finite time or converges smooth...It is shown that any solution to the semilinear problem{u（x,0=）u0（x）〈1,x∈[-1,1] u（±1,t）=0,t∈（0,T）, ut=uxx＋δ（1-u）^-p（x,t）∈（-1,1） ×（0,T）either touches 1 in finite time or converges smoothly to a steady state as t -~ ~e. Some extensions of this result to higher dimensions are also discussed.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10801058)an Earmarked Grant for Research, Hong Kong and a self-determined Research Fund of CCNU from the Colleges’ Basic Research and Operation of MOE
文摘It is shown that any solution to the semilinear problem{u（x,0=）u0（x）〈1,x∈[-1,1] u（±1,t）=0,t∈（0,T）, ut=uxx＋δ（1-u）^-p（x,t）∈（-1,1） ×（0,T）either touches 1 in finite time or converges smoothly to a steady state as t -~ ~e. Some extensions of this result to higher dimensions are also discussed.
