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Feb 27, 2017 at 2:44 comment added Abhi. A Thanks Igor, It looks like your method might be the way forward!
Feb 27, 2017 at 1:30 comment added Igor Khavkine If you are stuck with your operators $d$ and $\delta$, there's not much you can do. You can perhaps try to put $\delta d$ it in the form of a first order symmetric hyperbolic system, which also has a well studied initial value problem (see here for an entrance to the literature). My advice is still, unless you are absolutely constrained otherwise, to consider the operators $(\nabla v)$ and $Df$ from my answer instead of your $d v$ and $\delta f$.
Feb 27, 2017 at 1:14 history edited Abhi. A CC BY-SA 3.0
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Feb 26, 2017 at 17:46 history answered Abhi. A CC BY-SA 3.0