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A method is described in this chapter for constructing solutions, in the class of BV functions, of the initial value problem for hyperbolic systems of conservation laws by tracking the waves and monitoring their interactions as they collide. Interactions between shocks are easily resolved by solving Riemann problems; this is not the case, however, with interactions involving rarefaction waves. The random choice method, expounded in Chapter XIII, side-steps this difficulty by stopping the clock before the onset of wave collisions and reapproximating the solution by step functions.

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The Front Tracking Method and the Standard Riemann Semigroup

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  • 发表日期：

    2026年

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  • Constantine M. Dafermos

摘要

A method is described in this chapter for constructing solutions, in the class of BV functions, of the initial value problem for hyperbolic systems of conservation laws by tracking the waves and monitoring their interactions as they collide. Interactions between shocks are easily resolved by solving Riemann problems; this is not the case, however, with interactions involving rarefaction waves. The random choice method, expounded in Chapter XIII, side-steps this difficulty by stopping the clock before the onset of wave collisions and reapproximating the solution by step functions.