Chapter 13.2, Problem 13E

A circular plate is a composite of two different materials in the form of concentric circles. See Figure 13.2.7 on page 514. The temperature u(r, t) in the plate is determined from the boundary-value problem

$\begin{array}{l}\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}=\frac{\partial u}{\partial t},0<r<2,t>0\\ u(2,t)=100,t>0\\ u(r,0)=\{\begin{array}{ll}200,\hfill & 0<r<1\hfill \\ 100,\hfill & 1\le r<2.\hfill \end{array}\end{array}$

Figure 13.2.7 Composite circular plate in Problem 13