Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms

@article{Fan2000ZeroRL,
  title={Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms},
  author={Haitao Fan and Shi Jin and Zhen-huan Teng},
  journal={Journal of Differential Equations},
  year={2000},
  volume={168},
  pages={270-294}
}
Abstract In this paper we study the zero reaction limit of the hyperbolic conservation law with stiff source term ∂ t u+∂ x f(u)= 1 e u(1−u 2 ). For the Cauchy problem to the above equation, we prove that as e→0, its solution converges to piecewise constant (±1) solution, where the two constants are the two stable local equilibria. The constants are separated by either shocks that travel with speed 1 2 (f(1)−f(−1)), as determined by the Rankine-Hugoniot jump condition, or a non-shock… 

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