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Is the heat equation (e.g. 2D) solvable without boundary conditions? Or are the boundary conditions always present?

I've been puzzled a bit, since it seems that w/o boundary conditions there's no evolution from initial state. But this is what I'm trying to clarify.

mavavilj
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  • The boundary conditions are required to fix the solution... If you don't set the boundary conditions the solution is not unique. Unless there is no boundary... – PierreCarre Apr 22 '21 at 11:52
  • I think there is a convolution integral solution for the heat conduction problem, at least in 1D, that only needs the initial condition. – Benjamin_Gal Apr 22 '21 at 11:55
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    Think physically: if you don't know whether someone is heating, say, a brick from a side, how can you predict its temperature? That's what boundary conditions are about. – lisyarus Apr 22 '21 at 11:55
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    @Benjamin_Gal The convolution integral is in the whole space... In general we do need the boundary conditions. – PierreCarre Apr 22 '21 at 14:52

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