Positive temperatures on a semi-infinite rod-猫眼课题宝

半无限棒上的正温度

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1953

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D. Widder

其中a(Y)是非递减的。后来，P.Hartman和A.Wintner[1950；367]得到了有限杆(a&lt；x&lt；b)温度的类似结果。本文的目的是研究半无限长杆(0&lt；x&lt；°)的相应问题。对于半无限长杆，有两个经典问题可以表述如下：a.如果杆的初始温度为f(X)，如果有限端部温度为0，则确定杆的后续温度；u(x，0)=/(X)，u(0，t)=0。B.如果初始温度为0，并且有限端部保持可变温度(p(T)；u(x，0)=0，u(0，t)=&lt；p(T))，则确定随后的温度。在边界函数的适当条件下，已知解为(比较H.S.Carslaw和J.C.Jaeger[1948；40-44])：

where a(y) is nondecreasing. Later P. Hartman and A. Wintner [1950; 367] obtained analogous results for temperatures of a finite rod (a<x<b). It is the purpose of the present paper to investigate the corresponding questions for the half-infinite rod (0<x< °°). There are two classical problems for the semi-infinite rod which may be phrased as follows: A. Determine the subsequent temperatures of the rod if it is initially at temperature f(x) and if the finite end is held at temperature 0; u(x, 0) =/(x), u(0, t) = 0. B. Determine the subsequent temperatures if it is initially at temperature 0 and if the finite end is maintained at a variable temperature (p(t); u(x, 0) =0, u(0,t)=<p(t).^ Under suitable conditions on the boundary functions the solutions are known to be (compare H. S. Carslaw and J. C. Jaeger [1948; 40-44]):

Positive temperatures on a semi-infinite rod

半无限棒上的正温度

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