Strong well-posedness of a three phase problem with nonlinear transmission condition

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2012
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We prove existence and uniqueness of strong solutions to a quasilinear parabolic-elliptic system modelling an ionic exchanger. This chemical system consists of three phases connected with nonlinear boundary conditions. The most interesting difficulty of our problem manifests in the nonlinear transmission condition, as almost all quantities are non-linearly involved in this boundary equation. Our approach is based on the contraction mapping principle, where maximal Lp-regularity of the associated linear problem is used to obtain a fixed point equation of the starting problem.

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ISO 690KOTSCHOTE, Matthias, 2012. Strong well-posedness of a three phase problem with nonlinear transmission condition. In: Mathematical Methods in the Applied Sciences. 2012, 35(4), pp. 384-397. ISSN 0170-4214. eISSN 1099-1476. Available under: doi: 10.1002/mma.1565
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@article{Kotschote2012Stron-25562,
  year={2012},
  doi={10.1002/mma.1565},
  title={Strong well-posedness of a three phase problem with nonlinear transmission condition},
  number={4},
  volume={35},
  issn={0170-4214},
  journal={Mathematical Methods in the Applied Sciences},
  pages={384--397},
  author={Kotschote, Matthias}
}
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