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Mar 25, 2022 at 9:22 history edited Martin Sleziak CC BY-SA 4.0
http -> https (the question was bumped anyway)
Oct 23, 2012 at 9:03 history edited Igor Khavkine CC BY-SA 3.0
added 1347 characters in body
Oct 23, 2012 at 8:30 comment added MAK yes, as you said
Oct 23, 2012 at 8:25 comment added Igor Khavkine Ah, I see now. The $D^i u(0,x)$ should have been $D^i_t u(0,x)$ in your question.
Oct 23, 2012 at 8:21 comment added MAK for the sake of brevity, let me take $u_0(x)=x^n$, $n$ is a positive integer, and $u_1(x)=u_2(x)=u_3(x)=0$.
Oct 23, 2012 at 7:27 comment added Igor Khavkine To be honest, I'm not sure I understand your initial onditions. How are you specifying the values of the 0th-3rd time derivatives at $t=0$ needed to fix a unique solution?
Oct 23, 2012 at 6:53 comment added MAK @Igor, thank you very much. Indeed, it is easy to solve the non-homogeneous iterated equation. But, how shoold we choose the initial condition for $L_m u=v$ such that the solution of (auxiliary) second order EDP satisfies both the iterated EDP and the four initial conditions?
Oct 22, 2012 at 22:47 history answered Igor Khavkine CC BY-SA 3.0