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

Michael Dreher, Johannes Schnur

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Abstract

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.
Original languageEnglish
Pages (from-to)3016–3034
Number of pages19
JournalMathematical Methods in the Applied Sciences
Volume39
Issue number11
Early online date26 Oct 2015
DOIs
Publication statusPublished - Jul 2016

Keywords

  • viscous quantum hydrodynamics
  • stationary problem
  • existence of solutions

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