Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics

Michele, Federica Di; Mei, Ming; Rubino, Bruno; Sampalmieri, Rosella

doi:10.1016/j.jde.2017.03.032

Cited by 14 publications

(8 citation statements)

References 28 publications

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“…Unterreiter [30] proved the existence of the thermal equilibrium solution of the bipolar isentropic QHD model confined to a bounded domain by variational analysis, and the semi-classical limit is carried out recovering the minimizer of the limiting functional. This result recently was developed by Di Michele, Mei, Rubino and Sampalmieri [22] to a new model of the bipolar isentropic hybrid quantum hydrodynamics. Regarding the unipolar QHD model for irrotational fluid in spatial periodic domain, the global existence of the dynamic solutions and the exponential convergence to their equilibria were artfully proved by Li and Marcati in [18].…”

Section: Introductionmentioning

confidence: 74%

Stability and semi-classical limit in a semiconductor full quantum hydrodynamic model with non-flat doping profile

Hu,

Zhang

2017

Preprint

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We present the new results on stability and semi-classical limit in a semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping profile. The FQHD model can be used to analyze the thermal and quantum influences on the transport of carriers (electrons or holes) in semiconductor device. Inspired by the physical motivation, we consider the initialboundary value problem of this model over the one-dimensional bounded domain and adopt the ohmic contact boundary condition and the vanishing bohmenian-type boundary condition. Firstly, the existence and asymptotic stability of a stationary solution are proved by Leray-Schauder fixed-point theorem, Schauder fixed-point theorem and the refined energy method.Secondly, we show the semi-classical limit results for both stationary solutions and global solutions by the elaborate energy estimates and the compactness argument. The strong convergence rates of the related asymptotic sequences of solutions are also obtained.

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Section: Introductionmentioning

confidence: 74%

Stability and semi-classical limit in a semiconductor full quantum hydrodynamic model with non-flat doping profile

Hu,

Zhang

2017

Preprint

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“…In this section we present a new hybrid quantum hydrodynamic model accounting for a discontinuous pressure functional and the relaxation time. The hybrid model has been basically derived using the approach proposed in Ancona and Iafrate [25] for the standard fully quantum system, and recently used in Chiarelli et al [9] Michele et al [10][11][12] in the context of quantum hybrid models for semiconductors. In the present paper we introduce and study the one-dimensional case on the bounded domain O = ½0, 1.…”

Section: An H-qhd Model With Discontinuous Pressure Functional and Relaxation Timementioning

confidence: 99%

“…We recall the quantum effect function Q : O ! ½0, 1, introduced in Chiarelli et al [9] and Di Michele et al [10,11], which is a smooth function that indicates where the internal energy depends on the gradient of the charge density.…”

Section: An H-qhd Model With Discontinuous Pressure Functional and Relaxation Timementioning

confidence: 99%

“…A similar strategy was also employed in Di Michele et al [8] with application to electrolyte-oxide-semiconductor (EOS) devices. In the present paper, instead of using two different models in the classical and in the quantum domain, we adopt the fully hybrid approach firstly introduced in Chiarelli et al [9] and then developed in Di Michele et al [10][11][12]. In particular, we improve the results in Di Michele et al [10] allowing some parameters of the problem, namely the temperature T and the relaxation time t, to be non-constant, assuming different values within the classical and quantum domains.…”

Section: Introductionmentioning

confidence: 99%

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Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time

Michele

Mei

Rubino

et al. 2018

Mathematics and Mechanics of Solids

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In this paper we propose a generalization of the hybrid model for semiconductors already discussed by Chiarelli et al.and Di Michele et al., including a non-constant pressure functional and relaxation time. Roughly speaking, we assume that the normalized electron temperature and the relaxation time in the classical and quantum domains are different from each other. We derive the model heuristically, introducing a generalization of the stress tensor, which accounts for an interface contribute, and afterwards we prove the existence and uniqueness of weak solutions for such a new hybrid model. We apply the approach proposed by Di Michele et al. to obtain the stationary solutions to our problem, namely we prove the existence of the solution for a regularized problem, then we achieve the existence of a weak solution for the hybrid problem as a proper limit of the regular solution previously obtained.

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“…Besides, the semiconductor‐type models are also related to the fourth‐order degenerate partial differential equations. Specially, the hybrid quantum drift‐diffusion model and the hybrid quantum hydrodynamics model can be considered as a fourth‐order parabolic problem with boundary‐degeneracy coefficient (see Michele et al 6 ). Technically, the comparison principle and maximum principle are not valid for the higher‐order partial differential equations, and so it is necessary to introduce some new methods or techniques.…”

Section: Introductionmentioning

confidence: 99%

Study of weak solutions to a nonlinear fourth‐order parabolic equation with boundary degeneracy

Liang

Wang

2022

Math Methods in App Sciences

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A double degenerate fourth-order parabolic equation with a nonlinear secondorder diffusion from thin film theory is introduced, and the existence of weak solutions for the boundary degeneracy problem is studied. For this purpose, a non-degenerate fourth-order elliptic problem is constructed, and the corresponding existence and uniqueness are given by the variational method. From it, two kinds of approximate solutions are defined and then the existence and uniqueness of weak solutions for the related non-degenerate parabolic problem are shown by the iterative estimate, energy method, and compactness argument.Finally, the parabolic problem with boundary degeneracy is solved by applying energy estimate and several limit procedures.

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Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics

Cited by 14 publications

References 28 publications

Stability and semi-classical limit in a semiconductor full quantum hydrodynamic model with non-flat doping profile

Stability and semi-classical limit in a semiconductor full quantum hydrodynamic model with non-flat doping profile

Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time

Study of weak solutions to a nonlinear fourth‐order parabolic equation with boundary degeneracy

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