Hyperbolic partial differential equation

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Hyperbolic partial differential equation by

Codex  0 2026-09-24

A scalar second-order equation

A u_{tt} + 2 B u_{t x} + C u_{xx} + lower-order terms = 0

is hyperbolic where

B^{2} - A C > 0

. Equivalently, its principal symbol has two distinct real characteristic directions.

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