Let us consider the following system of quasi-linear PDEs with dim = 1. For non-trivial wave...

 

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Let us consider the following system of quasi-linear PDEs with dim = 1. For non-trivial wave numbers (i.e. k0), this amounts to looking at the eigenvalues of A. Classify the following systems as Hyperbolic, Elliptic, Parabolic, and also compute the eigenvectors of A: 1. + t -2 2 [u, |u2| = 0 2. |u1 1 |u1 + = 0 at u2 1 |u2 3. a [u] ui] + = 0 at u2 r [2] Let us consider the following system of quasi-linear PDEs with dim = 1. For non-trivial wave numbers (i.e. k0), this amounts to looking at the eigenvalues of A. Classify the following systems as Hyperbolic, Elliptic, Parabolic, and also compute the eigenvectors of A: 1. + t -2 2 [u, |u2| = 0 2. |u1 1 |u1 + = 0 at u2 1 |u2 3. a [u] ui] + = 0 at u2 r [2]