Abstract
The electrostatic potential describing the fields interior to a magnetohydrodynamic (MHD) power generating channel obeys a linear uniformly elliptic partial differential equation. The physically natural boundary conditions, however, do not fall within a class for which the solution has previously been shown to be unique. We discuss the boundary conditions appropriate to this situation and then generalize the discussion in Courant and Hilbert to demonstrate the uniqueness of the solution to an extended class of boundary value problems which includes the MHD channel as a special case.
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