Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations
Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations
复制标题
某些奇异抛物线方程弱解的 Harnack 估计和消光剖面
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Y. Kwong
中科院分区：
文献类型：
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作者：
E. DiBenedetto;Y. Kwong
我们为下面的奇异方程 (1.1) 的非负弱解建立了内在 Harnack 估计，其中 m 在最佳范围 ((N 2)+/N, 1) 内。本质意味着，由于奇点，抛物线几何中的时空维度必须通过解本身确定的因子重新缩放。结果是，当 t 接近灭绝时间时，对解和衰减率的急剧估计。 p-拉普拉斯型方程显示了类似的结果。
We establish an intrinsic Harnack estimate for nonnegative weak solutions of the singular equation (1.1) below, for m in the optimal range ((N 2)+/N, 1) . Intrinsic means that, due to the singularity, the space-time dimensions in the parabolic geometry must be rescaled by a factor determined by the solution itself. Consequences are, sharp supestimates on the solutions and decay rates as t approaches the extinction time. Analogous results are shown for p-laplacian type equations.