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Large data solutions to the viscous quantum hydrodynamic model with barrier potential

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2016

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https://doi.org/10.1002/mma.3749
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Mathematical Methods in the Applied Sciences. 2016, 39(11), pp. 3016-3034. ISSN 0170-4214. eISSN 1099-1476. Available under: doi: 10.1002/mma.3749

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We discuss analytically the stationary viscous quantum hydrodynamic model including a barrier potential, which is a nonlinear system of partial differential equations of mixed order in the sense of Douglis–Nirenberg. Combining a reformulation by means of an adjusted Fermi level, a variational functional, and a fixed point problem, we prove the existence of a weak solution. There are no assumptions on the size of the given data or their variation. We also provide various estimates of the solution that are independent of the quantum parameters.

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510 Mathematik

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ISO 690DREHER, Michael, Johannes SCHNUR, 2016. Large data solutions to the viscous quantum hydrodynamic model with barrier potential. In: Mathematical Methods in the Applied Sciences. 2016, 39(11), pp. 3016-3034. ISSN 0170-4214. eISSN 1099-1476. Available under: doi: 10.1002/mma.3749
BibTex
@article{Dreher2016Large-35380,
  year={2016},
  doi={10.1002/mma.3749},
  title={Large data solutions to the viscous quantum hydrodynamic model with barrier potential},
  number={11},
  volume={39},
  issn={0170-4214},
  journal={Mathematical Methods in the Applied Sciences},
  pages={3016--3034},
  author={Dreher, Michael and Schnur, Johannes}
}
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