## CHAPTER9

## Systems of One-Dimensional Nonlinear Partial Differential Equations

In earlier chapters, all of the problems involved one dependent variable as a function of one, two, or three independent variables. Here we introduce problems in which two dependent variables must be solved simultaneously to predict the evolution of a system. Examples include open channel flows in which the water velocity and depth are interdependent, lava flows in which the velocity depends upon a temperature-dependent lava rheology, and chemical systems in which two or more species are undergoing transport and reaction. Although systems of this sort are more complicated, their derivations require no new concepts; one need only ensure that the final well-posed problem ...