Conservation Equations and Characteristics

A conservation law for a physical system states that a certain quantity (e.g., mass, energy, or momentum) is independent of time. For continuous systems such as fluids or gases, these global quantities can be defined as integrals of density functions. The conservation law then translates into a local form, as a PDE for the density function. In this section we will study some first-order PDE that arise from conservation laws. We introduce a classic technique, called the method of characteristics, for analyzing these equations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.