Hyperbolic System of Partial Differential Equations
Consider the following system of first order partial differential equations for unknown functions, where
are once continuously differentiable functions, nonlinear in general.
Now define for each a matrix
We say that the system is hyperbolic if for all the matrix has only real eigenvalues and is diagonalizable.
If the matrix has distinct real eigenvalues, it follows that it's diagonalizable. In this case the system is called strictly hyperbolic.
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