Work

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

Year: 2025

Type: article

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 were proved 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 (Evol Equ Control Theory 5(1):147–184, 2016).

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01117-2

Authors: Annegret Glitzky, Matthias Liero

Institution: Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Deutsche Forschungsgemeinschaft, Berlin Mathematics Research Center MATH+