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Is it possible to solve this differential equation analytically?

Harry Peter
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user132682
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  • You can use separation of variables, but you may need the second order derivative for a boundary condition. – Chinny84 Mar 03 '14 at 07:59
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    Is $L_2(t)$ specified? That's the sticking point: BTW it makes separation of variables impossible. – Robert Israel Mar 03 '14 at 16:02
  • I have the feeling that the corresponding elliptic equation has no solution in $L^2(0L)$ (let alone on an interval with moving boundary), i.e., the spectrum of the differential operator is too large for the third derivative to generate a semigroup on $L^2(0,L)$; and therefore there is no solution for general $F_0$. – DeM Jan 13 '16 at 15:56

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