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

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2014
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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 solutions. 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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Fachgebiet (DDC)
510 Mathematik
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partielle Differentialgleichungen
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ISO 690DREHER, Michael, Johannes SCHNUR, 2014. Large data solutions to the viscous quantum hydrodynamic model with barrier potential
BibTex
@techreport{Dreher2014Large-27503,
  year={2014},
  series={Konstanzer Schriften in Mathematik},
  title={Large data solutions to the viscous quantum hydrodynamic model with barrier potential},
  number={328},
  author={Dreher, Michael and Schnur, Johannes}
}
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