Solvability for a drift-diffusion system with Robin boundary conditions

Heibig, Arnaud; Petrov, Adrien; Reichert, Christian

doi:10.1016/j.jde.2019.03.015

Journal of Differential Equations

2019

DOI: 10.1016/j.jde.2019.03.015

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Solvability for a drift-diffusion system with Robin boundary conditions

Arnaud Heibig

Adrien Petrov

Christian Reichert

Abstract: This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L 1 , L 2 and trace estimates. Finally, two examples coming from the corrosion and the self-gravitation model are analyzed.

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2023

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Cited by 2 publications

References 26 publications

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An overview of differential models for corrosion of cultural heritage artefacts

Frasca-Caccia,

Valentino,

Colace

et al. 2023

Math. Model. Nat. Phenom.

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New technologies play a central role in damage prevention of artistic and cultural heritage. The literature is flourishing of mathematical models that describe the process of corrosion due to weathering and exposition to pollutants. These models consist of differential equations or partial differential equations that need to be solved approximately by numerical methods. This paper aims to describe the mathematical models in the literature and the numerical methods used for their solution. We focus in particular on the studies of corrosion of pieces of art made of stone, lime mortar concrete and metal.

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An overview of differential models for corrosion of cultural heritage artefacts

Frasca-Caccia,

Valentino,

Colace

et al. 2023

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

Three-species drift-diffusion models for memristors

Jourdana

Jüngel

Zamponi

2023

Math. Models Methods Appl. Sci.

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A system of drift-diffusion equations for the electron, hole, and oxygen vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet–Neumann boundary conditions. This system describes the dynamics of charge carriers in a memristor device. Memristors can be seen as nonlinear resistors with memory, mimicking the conductance response of biological synapses. In the fast-relaxation limit, the system reduces to a drift-diffusion system for the oxygen vacancy density and electric potential, which is often used in neuromorphic applications. The following results are proved: the global existence of weak solutions to the full system in any space dimension; the uniform-in-time boundedness of the solutions to the full system and the fast-relaxation limit in two space dimensions; the global existence and weak–strong uniqueness analysis of the reduced system. Numerical experiments in one space dimension illustrate the behavior of the solutions and reproduce hysteresis effects in the current–voltage characteristics.

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Solvability for a drift-diffusion system with Robin boundary conditions

Cited by 2 publications

References 26 publications

An overview of differential models for corrosion of cultural heritage artefacts

An overview of differential models for corrosion of cultural heritage artefacts

Three-species drift-diffusion models for memristors

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