We want to measure heat flow in an insulated sphere of radius
R
when there is spherical symmetry. We have
u=u(t,rho)
with
u t=κ(urhorho+ 2/rho urho)
urho(t,R)=0
u(0,rho)=f(rho).
Use
−λ^2
for the separation constant. Don't forget to check the zero eigenvalue! a) You will get a transcendental equation for the non-zero eigenvalues, Use Mathematica to find the first 3 non-zero eigenvalues
t least 5 decimal places. b) Find the general solution to the problem and formulas for all coefficients in terms of the initial data. c) The zero eigenvalue should give you a constant solution. What does the coefficient for this term represent?
