Partial Differential Equations
The Rankine-Hugoniot conditions describe the mathematical relationships that govern the behavior of discontinuities, or shocks, in solutions of nonlinear first-order partial differential equations. These conditions provide a way to determine how characteristics intersect and how physical quantities such as mass, momentum, and energy are conserved across a shock wave. They are crucial in analyzing and solving problems involving shock waves in various fields like fluid dynamics and gas dynamics.
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