| Summary: | 碩士 === 東海大學 === 應用數學系 === 102 === This article concerns with the Riemann problem of conservation laws. Generally, there are infinitely many solutions to conservation laws, but only one solution satisfies the entropy condition. Therefore, we focus on the solution satisfying the entropy condition. Chapter 1-3 introduce the characteristic method for the scalar equation, shock waves, rarefaction waves, and entropy conditions. They are illustrated by the Burger equation. Chapter 4 considers the solution of the linear systems and explains the solution of the Riemann problem in the phase plane. Chapter 5 considers the nonlinear system, illustrated by the isothermal equation, which comes from the simplified Euler equations.
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