parabolic differential equation

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parabolic differential equation [¦par·ə¦bäl·ik ‚dif·ə′ren·chəl i′kwā·zhən]

(mathematics)

A general type of second-order partial differential equation which includes the heat equation and has the formwhere theA_i_j,B_i,C, andFare suitably differentiable real functions ofx₁,x₂, …,x_n, and there exists at each point (x₁, …,x_n) a real linear transformation on thex_iwhich reduces the quadratic formto a sum of fewer thannsquares, not necessarily all of the same sign, while the same transformation does not reduce theB_ito 0. Also known as parabolic partial differential equation.

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