Good morning,
I'm interested in solving a Cauchy problem for the iterated singular EPD.
Well, Weinstein (On a class of PDEs of even order, 1955) showed how the decomposition formula leads to the solution of the Cauchy problem for the iterated wave equation (so, for $k=0$).
My question, how one can use this decomposition to solve a Cauchy problem for the iterated EPD equation?
$L_kL_m u(t,x)=0$,
$D^i D_t^i u(0,x)=u_i(x) , 0\leq i\leq 3 \ $,
where $L_k := D^2_t-D^2_x+ \frac{k}{t}D_t$
Thanks in advance
