WIAS Preprint No. 3142, (2024)

Uniqueness and regularity of weak solutions of a drift-diffusion system for perovskite solar cells


Authors

  • Glitzky, Annegret
    ORCID: 0000-0003-1995-5491
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915

2020 Mathematics Subject Classification

  • 35K20 35K55 35B65 78A35 35Q81

Keywords

  • Drift-diffusion system, charge transport, uniqueness of weak solutions, regularity theory, perovskite solar cells, non-Boltzmann statistics

DOI

10.20347/WIAS.PREPRINT.3142

Abstract

We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac statistics for electrons and holes and Blakemore statistics for the mobile ionic vacancies in the perovskite. Existence of weak solutions and their boundedness was proven in a previous work. For the uniqueness proof, we establish improved integrability of the gradients of the charge-carrier densities. Based on estimates obtained in the previous paper, we consider suitably regularized continuity equations with partly frozen arguments and apply the regularity results for scalar quasilinear elliptic equations by Meinlschmidt & Rehberg, Evolution Equations and Control Theory, 2016, 5(1):147-184.

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