# parabolic differential equation

## 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 form where the

*A*_{i }_{j },*B*_{i },*C*, and*F*are suitably differentiable real functions of*x*_{1},*x*_{2}, …,*x*_{n }, and there exists at each point (*x*_{1}, …,*x*_{n }) a real linear transformation on the*x*_{i }which reduces the quadratic form to a sum of fewer than*n*squares, not necessarily all of the same sign, while the same transformation does not reduce the*B*_{i }to 0. Also known as parabolic partial differential equation.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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