Relaxation limit and initial layer to hydrodynamic models for semiconductors

Nishibata, Shinya; Suzuki, Masahiro

doi:10.1016/j.jde.2010.06.008

Cited by 15 publications

(5 citation statements)

References 24 publications

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“…The relaxation limit of the Euler-Poisson system to the drift-diffusion equations, which has been studied in [25], has been solved in [14,16,17] for weak entropy solutions. The same limit has been studied in [28] in a one-dimensional domain, proving the decay of the initial layer which develops for initial data not in equilibrium. For smooth solutions, Luo et al [23], Hsiao and Yang [13] and Li et al [22] investigated the asymptotic behaviour of solutions to the Cauchy and initial boundary value problem, respectively.…”

Section: Introductionmentioning

confidence: 62%

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

Alì

Chen

2011

Nonlinearity

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The Euler-Poisson system consists of the balance laws for electron density and current density coupled to the Poisson equation for the electrostatic potential. The limit of vanishing electron mass of this system with both well-and ill-prepared initial data on the whole space case is discussed in this paper.Although it has some relations to the incompressible limit of the Euler equations, i.e. the limit velocity satisfies the incompressible Euler equations with damping, things are more complicated due to the linear singular perturbation including the coupling with the Poisson equation. A careful analysis on the structure of the linear perturbation has been done so that we are able to show the convergence for well-prepared initial data and ill-prepared initial data where the convergence occurs away from time t = 0.

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Section: Introductionmentioning

confidence: 62%

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

Alì

Chen

2011

Nonlinearity

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“…In the papers [13,15], singular limit problem with initial layer is considered between the Boltzmann equation and the compressible Euler equations obtained as the first approximation of the Chapman-Enskog expansion. For model systems of semi-conductors, the singular limit problem from hydrodynamic model to drift-diffusion model associated with stationary waves is considered in the paper [12].…”

Section: Singular Limitmentioning

confidence: 99%

Viscous shock profile and singular limit for hyperbolic systems with Cattaneo's law

Nakamura¹,

Kawashima

2018

Kinetic &Amp; Related Models

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In the current paper, we consider large time behavior of solutions to scalar conservation laws with an artificial heat flux term. In the case where the heat flux is governed by Fourier's law, the equation is scalar viscous conservation laws. In this case, existence and asymptotic stability of one-dimensional viscous shock waves have been studied in several papers. The main concern in the current paper is a 2 × 2 system of hyperbolic equations with relaxation which is derived by prescribing Cattaneo's law for the heat flux. We consider the one-dimensional Cauchy problem for the system of Cattaneo-type and show existence and asymptotic stability of viscous shock waves. We also obtain the convergence rate by utilizing the weighted energy method. By letting the relaxation time zero in the system of Cattaneo-type, the system is formally deduced to scalar viscous conservation laws of Fourier-type. This is a singular limit problem which occurs an initial layer. We also consider the singular limit problem associated with viscous shock waves.

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“…[15][16][17][18][19][20] In these regimes, a complicated system may asymptotically be replaced by a much simpler hyperbolic or parabolic system, the behavior of the latter is either already well understood or easier to analyze.…”

Section: J Yangmentioning

confidence: 99%

Combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations

Yang

2014

Applicable Analysis

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This paper is devoted to study the combined relaxation and non-relativistic limit of non-isentropic Euler-Maxwell equations with relaxation for semiconductors and plasmas. We prove that, as the relaxation time tends to zero and the light speed tends to infinite, periodic initial-value problem of a certain scaled non-isentropic Euler-Maxwell equations has unique smooth solution existing in the time interval where the corresponding classical driftdiffusion model has smooth solutions. It is shown that the relaxation regime plays a decisive role in the combined limit. Furthermore, the corresponding convergence rate is obtained.

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Relaxation limit and initial layer to hydrodynamic models for semiconductors

Cited by 15 publications

References 24 publications

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data

Viscous shock profile and singular limit for hyperbolic systems with Cattaneo's law

Combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations

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