Critical Thresholds in a Convolution Model for Nonlinear Conservation Laws

@article{Liu2001CriticalTI,
  title={Critical Thresholds in a Convolution Model for Nonlinear Conservation Laws},
  author={Hailiang Liu and Eitan Tadmor},
  journal={SIAM J. Math. Analysis},
  year={2001},
  volume={33},
  pages={930-945}
}
In this work we consider a convolution model for nonlinear conservation laws. Due to the delicate balance between the nonlinear convection and the nonlocal forcing, this model allows for narrower shock layers than those in the viscous Burgers’ equation and yet exhibits the conditional finite time breakdown as in the damped Burgers’ equation. We show the critical threshold phenomenon by presenting a lower threshold for the breakdown of the solutions and an upper threshold for the global… CONTINUE READING

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