What do You Stand For?. A PDE is a Partial Differential Equation This is an equation with derivatives of at least two variables in it. In general, partial differential equations are much more difficult to solve analytically than are ordinary differential equations. What Does a PDE Look Like. Let
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Ω0 : a three-dimensional acoustic region,
S0 : a plate region,
Γ0=∂Ω0＼S0 : a part of the boundary of the acoustic field,
∂S0 : the boundary of the plate,
P0 : the acoustic pressure in Ω0,
U0 : the vertical plate displacement,
c : the sound velocity,
ρ0 : the air mass density,
D : the flexural rigidity of plate,
ρ1 : the plate mass density,
n : the outward normal vector on ∂Ω from Ω0, and
σ : the outward normal vector on ∂S0 from S0.