A. Jüngel, P. Kristöfel:

"Lyapunov functionals, weak sequential stability, and uniqueness analysis for energy-tranport systems";

in: "ASC Report 06/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

A class of strongly coupled parabolic systems, modeling the energy transport

of electrons in semiconductors, is analyzed. The variables are the electron density and

the thermal energy. First, some Lyapunov functionals are derived, which yields the weak

sequential stability for smooth solutions in the sense of Feireisl, using weak compactness

results. Second, by the H−1 method, the uniqueness of bounded weak solutions is proved.

http://www.asc.tuwien.ac.at/preprint/2011/asc06x2011.pdf

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