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Finite difference scheme for unconfined aquifer equation ?

Finite difference scheme for unconfined aquifer equation ?

(OP)
For an unconfined aquifer , we have this pde for the water table position , of course after making the Boussinesq somehow linear :

∂²(h²)∕∂x² + ∂²(h²)∕∂y² = (2s/k ) ∂h/∂t - 2N/k

N and K and S are constants .

would u tell me what type mathematically it is ? this equation , in respect to h^2 seems elliptic , but physically its not? . cant we treat it and solve it like 2d heat equation ? I need to solve it numerically via finite difference .
and ADE method for 2D heat , seems ok .

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