Electro–Reaction–Diffusion Systems Including Cluster Reactions of Higher Order

Glitzky, Annegret; Huenlich, Rolf

doi:10.1002/1522-2616(200008)216:1<95::aid-mana95>3.3.co;2-8

Math. Nachr.

2000

DOI: 10.1002/1522-2616(200008)216:1<95::aid-mana95>3.3.co;2-8

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Electro–Reaction–Diffusion Systems Including Cluster Reactions of Higher Order

Annegret Glitzky

Rolf Huenlich

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2005

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“…At first we consider the case that each species has a constant charge number, Q i (ψ) = q i = const. Then we arrive at a model which we have studied in [13,8,9,10]. There we assumed that all species are mobile, l = m, that the diffusivities do not depend on b, and that the initial values are strongly positive, U i ≥ c > 0.…”

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confidence: 99%

Global Existence Result for Pair Diffusion Models

Glitzky

Hünlich²

2005

SIAM J. Math. Anal.

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In this paper we prove a global existence result for pair diffusion models in two dimensions. Such models describe the transport of charged particles in semiconductor heterostructures. The underlying model equations are continuity equations for mobile and immobile species coupled with a nonlinear Poisson equation. The continuity equations for the mobile species are nonlinear parabolic PDEs involving drift, diffusion, and reaction terms; the corresponding equations for the immobile species are ODEs containing reaction terms only. Forced by applications to semiconductor technology, these equations have to be considered with nonsmooth data and kinetic coefficients additionally depending on the state variables.Our proof is based on regularizations, on a priori estimates which are obtained by estimates of the free energy and by Moser iteration, as well as on existence results for the regularized problems. These are obtained by applying the Banach fixed point theorem for the equations of the immobile species, and the Schauder fixed point theorem for the equations of the mobile species.

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confidence: 99%

Global Existence Result for Pair Diffusion Models

Glitzky

Hünlich²

2005

SIAM J. Math. Anal.

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Electro–Reaction–Diffusion Systems Including Cluster Reactions of Higher Order

Cited by 1 publication

References 0 publications

Global Existence Result for Pair Diffusion Models

Global Existence Result for Pair Diffusion Models

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