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Under ideal assumptions, what is the two-dimensional heat equation?

Under ideal assumptions, what is the two-dimensional heat equation? Correct Answer ut = c2 ∇2 u = c2 (uxx + uyy)

Consider a rectangular plate (thermally conductive material), with dimensions a × b. The plate is heated and then insulated. We let u (x, y, t) = temperature of plate at position (x, y) and time t. For a fixed t, the height of the surface z = u (x, y, t) gives the temperature of the plate at time t and position (x, y). Under ideal assumptions (e.g. uniform density, uniform specific heat, perfect insulation, no internal heat sources etc.) one can show that u satisfies the two-dimensional heat equation, ut = c2 ∇2 u = c2 (uxx + uyy) for 0 < x < a, 0 < y < b.

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