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2nd Order
The general n-dimensional second order quasilinear equations:
where
is a symmetric matrix and
.
Classification is based on the eigenvalues of A:
- parabolic if any eigenvalues are zero; otherwise:
- elliptic if all eigenvalues are the same sign;
- hyperbolic if all eigenvalues except one are of the same sign;
- ultrahyperbolic, otherwise.
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