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Stationary solutions of two-dimensional heterogeneous energy models with multiple species. (English) Zbl 1235.35082

Biler, Piotr (ed.) et al., Nonlocal elliptic and parabolic problems. Papers of the conference, Bȩdlewo, Poland, September 12–15, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 66, 135-151 (2004).
Summary: 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.
For the entire collection see [Zbl 1052.35002].

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q60 PDEs in connection with optics and electromagnetic theory
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