We show how to associate to each analytic function f of one variable a complex conservation law. When written in terms of real variables, this equation turns into a symmetric hyperbolic system of two first order conservation laws in time and two space variables for two unknowns. The hope is that the theory of analytic functions can be exploited to study the properties of the solutions of these model equations. These systems are strictly hyperbolic where f' is unequal to zero, and nonlinear where f'' is unequal to zero. There is, however, in every state at least one direction of propagation which is not genuinely nonlinear. We then show that every 2 x 2 quasilinear first order hyperbolic system fails to be genuinely nonlinear in some direction of propagation. The notions of the first section are easily extended to analytic functions of several variables. (ERA citation 10:035874)
展开▼
