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On the convergence rate of vanishing viscosity approximations

Alberto Bressan Tong Yang

Analysis of PDEs mathscidoc:1912.43944

Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 57, (8), 1075-1109, 2004.8
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound u (t,) u (t,)= O (1)(1+ t) | ln | on the distance between an exact BV solution u and a viscous approximation u, letting the viscosity coefficient 0. In the proof, starting from u we construct an approximation of the viscous solution u by taking a mollification u* and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed . Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families. 2004 Wiley Periodicals, Inc.
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@inproceedings{alberto2004on,
  title={On the convergence rate of vanishing viscosity approximations},
  author={Alberto Bressan, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210822239871508},
  booktitle={Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences},
  volume={57},
  number={8},
  pages={1075-1109},
  year={2004},
}
Alberto Bressan, and Tong Yang. On the convergence rate of vanishing viscosity approximations. 2004. Vol. 57. In Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences. pp.1075-1109. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210822239871508.
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