Example 11.16. Find
at each point in the upper half-disk , if
the temperature at points on the boundary satisfies
Figure 11.19 The temperature in a half-disk.
Explore Solution 11.16.
Construct the solution via a known conformal mapping. This is similar to Example 11.9.
We can check out some of the boundary values by taking limits.
Use Mathematica to make a contour plot of the temperature.
Hence the temperature function is harmonic in the upper half-disk , and has the desired boundary values.
(c) 2006 John H. Mathews, Russell W. Howell