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Abstract: The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in . We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift–diffusion system under the combined relaxation and semiclassical limits. [Copyright &y& Elsevier]

Abstract: In this paper we establish the existence of a unique thermal equilibrium solution of the bipolar multidimensional quantum Euler–Poisson system over the whole space and obtain the relevant semiclassical limit and a combined Planck–Debye length limit through using energy estimating methods and a fixed point theory. [Copyright &y& Elsevier]