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Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics. (English) Zbl 1368.35262
The paper presents system of equations for two liquids motivated by the problem of quasi-hydrodynamic description of electrons and holes in a semiconductor. For this reason, an additional term associated with the quantum effects (within Bohmian formalism) is added to each of basic partial stationary (by assumption of the thermal equilibriom) differential equations. Further, the system is treated purely mathematically, and an existence of limit functions, which are the weak solutions to the system considered, is proven.

35Q82 PDEs in connection with statistical mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
82D37 Statistical mechanical studies of semiconductors
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
Full Text: DOI
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