I'm trying to solve this PDE problem:
on $[-1,1]$ with periodic boundary conditions, and taking as initial data the function $u_0=1+\sin^2(\pi x)+\sin^2(2\pi x)$
I want to obtain the analytic solution. I think i can solve it separating variables and applying Fourier after that, ¿but anyone knows a shorter or easier way to get the solution?
Thanks a lot.