Strict hyperbolicity

Summary

Strict hyperbolicity is a condition on a system of evolution equations that is stronger than hyperbolicity. For a first-order system $u_t + \sum_j A_j u_{x_j} = 0$ it asks that, in each direction, the matrix $\sum_j \xi_j A_j$ has real and distinct eigenvalues. The eigenvalues are the speeds of the different waves, and distinct speeds keep the waves apart. Strictly hyperbolic systems have a well-posed Cauchy problem, and they are the setting of the classical theory of hyperbolic conservation laws.