Long-Time Behaviour of Heat Flow: Global Estimates and Exact Asymptotics
Long-Time Behaviour of Heat Flow: Global Estimates and Exact Asymptotics
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热流的长期行为：全局估计和精确渐近
DOI：
10.1007/s002050050063
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发表时间：
1997
影响因子：
2.5
通讯作者：
J. Norris
中科院分区：
文献类型：
--
作者：
J. Norris
摘要 得到了椭圆二阶微分算子热核的全局上界和下界，该上界和下界在某些长时大空间渐近过程中变得尖锐。我们证明了阿伦森高斯界限的推广，它可以正确识别热流的有效漂移。在周期性系数的情况下，我们给出有效电导率的变分特征，然后使其出现在热核边界中。这些结果适用于具有可测量系数的热内核。对于可微系数，我们证明了更严格的估计，其中同质化率已知是最佳的。
Abstract We obtain global upper and lower bounds on the heat kernel of an elliptic second-order differential operator, which become sharp in certain long-time and large-space asymptotics. We prove a generalization of Aronson's Gaussian bounds which identifies correctly an effective drift for heat flow. In the case of periodic coefficients we give variational characterizations of the effective conductivity, which is then made to appear in heat kernel bounds. These results are for heat kernels with measurable coefficients. For differentiable coefficients we prove tighter estimates, in which the rate of homogenization is known to be optimal.