Chapter 12: Partial Differential Equations
boundary. The function u(x,y,t) measures the vertical displacement of the membrane (think of a drum for instance) and satisfies ∂2u ∂t2 = c2 ∂2u ∂x2 + ∂2u ∂y2 = c2∇2u, where c2 is proportional to the tension of the membrane. The boundary conditions (Dirichlet) are u = 0 on the boundary of the membrane and the initial conditions ...
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