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

Annegret Glitzky, and Rolf Hünlich. "Stationary solutions of two-dimensional heterogeneous energy models with multiple species." Banach Center Publications 66.1 (2004): 135-151. <http://eudml.org/doc/282554>.

@article{AnnegretGlitzky2004,
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 a 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.},
author = {Annegret Glitzky, Rolf Hünlich},
journal = {Banach Center Publications},
keywords = {energy models; mass; charge and energy transport in heterostructures; strongly coupled elliptic systems; mixed boundary conditions; implicit function theorem; existence; uniqueness; regularity},
language = {eng},
number = {1},
pages = {135-151},
title = {Stationary solutions of two-dimensional heterogeneous energy models with multiple species},
url = {http://eudml.org/doc/282554},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Annegret Glitzky
AU - Rolf Hünlich
TI - Stationary solutions of two-dimensional heterogeneous energy models with multiple species
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 135
EP - 151
AB - 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 a 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.
LA - eng
KW - energy models; mass; charge and energy transport in heterostructures; strongly coupled elliptic systems; mixed boundary conditions; implicit function theorem; existence; uniqueness; regularity
UR - http://eudml.org/doc/282554
ER -