| 摘要: |
| 讨论n维变系数二阶线性蜕化抛物型方程，在蜕化条件下利用抛物极值原理和不等式估计获得了该类抛物型微分方程的非负强解的Harnack性质．这一结论把一致抛物型方程的Harnack不等式推广到了一类新的蜕化抛物型微分方程，且所获Harnack不等式还可借助于三维抛物型微分方程的热传导性得以解释 |
| 关键词: 抛物型方程 蜕化 Harnack不等式 热传导性 |
| DOI： |
| 分类号:O175.2 |
| 基金项目:江苏省靖江市科技局与常州大学产学研合作项目(CDHJZ1509008) |
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| Abstract: |
| Some n-dimensional variable coefficient linear second order degenerate parabolic equations were discussed. Under certain degeneration conditions, the Harnack property for nonnegative strong solution of degenerate parabolic equations was obtained by parabolic maximum principle and inequality estimates. The obtained conclusion extended the Harnack inequality for uniformly parabolic equations to a class of degenerate parabolic equations. An interpretation was given to this Harnack inequality in terms of heat conduction property of three-dimensional parabolic equations. |
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