孙仁斌.一类对数形式退缩抛物型方程组解的整体存在性与爆破[J].中南民族大学学报自然科学版,2017,(1):119-122
一类对数形式退缩抛物型方程组解的整体存在性与爆破
Global Existence and Blow-up for a Degenerate Parabolic System Come from Logarithmic Function
  
DOI:
中文关键词: 退缩抛物型方程组  局部解  整体解  爆破
英文关键词: degenerate parabolic system  local solution  global solution  blow-up
基金项目:国家自然科学基金资助项目(61374085)
作者单位
孙仁斌 中南民族大学 数学与统计学学院武汉 430074 
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中文摘要:
      考虑了一类由对数函数产生的退缩抛物型方程组的初边值问题, 利用逼近的方法得到了解的局部存在 性. 通过特征函数构造的上解得到了解整体存在的条件, 利用特征函数得到了解在有限时刻爆破的条件及爆破时 间的上限.
英文摘要:
      In this paper, a class of initial-boundary value problem of degenerate parabolic system come from logarithmic function was considered. The local existence of solution was proved by approximation method. The condition of global existence of the solution was obtained by the upper solution of the characteristic function, and the blow-up condition and the upper bound of the blow-up time were obtained by using the characteristic function.
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