Fall 2010
The book is Mathematical Models in Biology by Leah Edelstein-Keshet, but I will be supplementing the material with lots of other things.
Suppose u_x(0,t)=u_x(Pi,t)=0.
Show that u(x,t) = c_n(t) cos(n x) where n is an integer solves this equation and write down the differential equation for c_n(t). For what values of (a,n,R) do solutions c_n(t) decay to zero as t increases?