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Asymptotic behavior of solutions to the bipolar hydrodynamic model of semiconductors in bounded domain. (English) Zbl 1255.82065

Summary: In this paper we present a physically relevant hydrodynamic model for a bipolar semiconductor device considering Ohmic conductor boundary conditions and a non-flat doping profile. For such an Euler-Poisson system, we prove, by means of a technical energy method, that the solutions are unique, exist globally and asymptotically converge to the corresponding stationary solutions. An exponential decay rate is also derived. Moreover we allow that the two pressure functions can be different.

MSC:

82D37 Statistical mechanics of semiconductors
35Q60 PDEs in connection with optics and electromagnetic theory
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
76R50 Diffusion
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