Hyperbolic conservation laws

Hyperbolic conservation laws are mathematical equations used to describe how certain quantities—like mass, momentum, or energy—move and evolve over time within a system, such as a fluid or gas. These laws assume that the amount of the quantity is conserved as it flows, meaning it cannot be created or destroyed. The term "hyperbolic" relates to the type of equations involved, which often predict wave-like phenomena such as shocks or shocks waves, where abrupt changes occur. They are fundamental in fields like fluid dynamics and traffic flow, helping us understand and predict how these quantities behave in real-world systems.