The radial heat equation with pole type data
The radial heat equation with pole type data
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具有极型数据的径向热方程
DOI：
10.1090/s0002-9904-1967-11681-1
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发表时间：
1967
影响因子：
1.3
通讯作者：
L. Bragg
中科院分区：
文献类型：
--
作者：
L. Bragg
在[<f>1]，[3]，[4]中，当（r）是增长（1，a）的全体时，得到了一些结果，这些结果在[3]中被推广到L2理论。本文给出了当数据函数ε（r）有极点但除此之外是整函数时（1）解的结构的一些结果.这些结构是根据卷积积分定义的，证明是基于（1）的解的拉普拉斯变换公式[2]和上面提到的展开理论。证明的细节将出现在即将发表的论文中，该论文也将讨论对数奇点。我们用什么表示？>（r，t; <！>（i））（1）的解定义为：
with A M = ^ + [ ( M ~ l)/r]Dr. Results have been obtained when <f>(r) is entire of growth (1, a) in r [ l ] , [3], [4] and these have been extended to the L2 theory in [3]. In this note, we state some results on the structures of solutions of (1) when the data function <£(r) has a pole a t r = 0 but is otherwise entire. These structures are defined in terms of convolution integrals and the proofs are based on the Laplace transform formulation [2] of solutions of (1) and the expansion theory referred to above. The details of the proofs will appear in a forthcoming paper that will also discuss logarithmic singularities. We denote by ?>(r, t; <!>(/)) the solution of (1) defined by