Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media

Jack Xin

Analysis of PDEs mathscidoc:1912.43858

Archive for rational mechanics and analysis, 128, (1), 75-103, 1994.3
We prove the existence of multidimensional traveling-wave solutions to the scalar equation for the transport of solutes (contaminants) with nonlinear adsorption and spatially periodic convection-diffusion-adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the Lax and Oleinik entropy conditions. In the nondegenerate case, we also prove the uniqueness of the traveling waves. These traveling waves are analogues of viscous shock profiles. They propagate with effective speeds that depend on the periodic porous media only up to their mean states, and are given by an averaged Rankine-Hugoniot relation. This is a direct consequence of the fact that the transport equation is in conservation form. We use the sliding domain method, the continuation method, spectral theory, maximum principles, and a priori estimates. In the degenerate case, the traveling waves are weak
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@inproceedings{jack1994existence,
  title={Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media},
  author={Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210238955696422},
  booktitle={Archive for rational mechanics and analysis},
  volume={128},
  number={1},
  pages={75-103},
  year={1994},
}
Jack Xin. Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media. 1994. Vol. 128. In Archive for rational mechanics and analysis. pp.75-103. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210238955696422.
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