Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques
Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques
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DOI：
10.1007/978-0-8176-4995-1
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发表时间：
2010-10
期刊：
影响因子：
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通讯作者：
O. Calin;D. Chang;Kenro Furutani;C. Iwasaki
中科院分区：
文献类型：
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作者：
O. Calin;D. Chang;Kenro Furutani;C. Iwasaki
傅里叶变换被认为是寻找具有常数系数的算子的基本解的最强大和最有用的方法之一。然而，在一般情况下，这种方法有其自身的局限性。本书介绍了其他几种可以与傅里叶变换方法同时使用的方法，以获得椭圆和次椭圆算子的热核。文本包含大量示例，有助于理解。为读者提供概述。抛物线算子理论描述了给定流形上的热量分布以及演化现象和扩散过程。抛物型偏微分方程初值问题的解取决于其热核，它是相关抛物型算子的基本解。因此，为这些内核找到明确的公式非常重要。
The Fourier transform is known as one of the most powerful and useful methods for finding fundamental solutions of operators with constant coefficients. However, in the general case this method has its own limitations. This book presents several other methods that can be used concurrently with the Fourier transform method to obtain heat kernels for elliptic and sub-elliptic operators. The text contains a large number of examples which facilitate understanding.An Overview for the Reader. The theory of parabolic operators describes the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. The solution of an initial value problem for a parabolic partial differential equation depends on its heat kernel, which is the fundamental solution of the associated parabolic operator. Hence the importance of finding explicit formulas for these kernels.