(a) Let B be the ball {x2 + y2 +z2 < a2}. Find all the
Chapter 10, Problem 8(choose chapter or problem)
(a) Let B be the ball {x2 + y2 +z2 < a2}. Find all the radial eigenfunctionsof inBwiththeNeumannBCs.Byradialwemean depending only on the distance r to the origin. [Hint: A simple method is to let v(r)=ru(r).] (b) Find a simple explicit formula for the eigenvalues. (c) Write the solution of ut =k u in B, ur =0 on bdy B,u(x,0)= (r)asaninniteseries,includingtheformulasforthecoefcients. (d) In part (c), why does u(x, t) depend only on r and t?
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