WIAS Preprint No. 896, (2003)

Stationary solutions of two-dimensional heterogeneous energy models with multiple species



Authors

  • Glitzky, Annegret
  • Hünlich, Rolf

Keywords

  • energy models, mass, charge and energy transport in heterostructures, strongly coupled elliptic systems, mixed boundary conditions, Implicit Function Theorem, existence, uniqueness, regularity

Abstract

We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of such a thermodynamic equilibrium there exists an unique steady state, too. Our proof is based on the Implicit Function Theorem and on regularity results for systems of strongly coupled elliptic differential equations with mixed boundary conditions and non-smooth data.

Appeared in

  • Banach Center Publ. bf 66 (2004), pp. 135--151.

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