Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors

Gasser, Ingenuin; Hsiao, Ling; Li, Hailiang

doi:10.1016/s0022-0396(03)00122-0

Cited by 78 publications

(69 citation statements)

References 28 publications

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“…we can obtain the following estimates by using a similar argument of [14]. Since the proof is tedious but similar as in the previous works, we only list the results and omit its details.…”

Section: Global Existence and Algebraical Decay Ratementioning

confidence: 78%

“…In conclusion, we have Theorem 3.4 Under the assumptions in Theorem 1.1, there exists a unique time global solution ( 1 , z 1 , 2 , z 2 ) of the IBVP (3.1) such that 11) and there exist positive constants C, a such that 14) and 4 The optimal convergence rate…”

Section: Global Existence and Algebraical Decay Ratementioning

confidence: 85%

“…In order to obtain the asymptotic behavior and optimal decay rate, noting that E = 1 -2 satisfies the damping "Klein-Gordon" equation (see [14,15]), we first obtain the exponential decay rate of the electric field E by energy methods. Then, we can establish the algebraical decay rate of the perturbed densities 1 and 2 .…”

Section: Theorem 12 Under the Assumptions Of Theorem 11 It Holds Thatmentioning

confidence: 99%

“…Gasser and Marcati [13] discussed the relaxation limit, quasineutral limit and the combined limit of weak solutions for the bipolar Euler-Poisson system. Gasser et al [14] investigated the large time behavior of solutions of Cauchy problem to the bipolar model basing on the fact that the frictional damping will cause the nonlinear diffusive phenomena of hyperbolic waves, while Huang and Li recently studied large-time behavior and quasineutral limit of L ∞ solution of the Cauchy problem in [15]. As far as we know, no results about the global existence and large time behavior to (1.2) with boundary effect can be found.…”

Section: Introductionmentioning

confidence: 99%

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Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

2012

Bound Value Probl

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“…we can obtain the following estimates by using a similar argument of [14]. Since the proof is tedious but similar as in the previous works, we only list the results and omit its details.…”

Section: Global Existence and Algebraical Decay Ratementioning

confidence: 78%

Section: Global Existence and Algebraical Decay Ratementioning

confidence: 85%

Section: Theorem 12 Under the Assumptions Of Theorem 11 It Holds Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

2012

Bound Value Probl

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“…Hattori and Zhu [23] proved the stability of steady-state solutions for a recombined one-dimensional bipolar hydrodynamical model. Gasser, Hsiao and Li [6] investigated the large time behavior of smooth "small" solutions of the initial value problem for the one-dimensional bipolar hydrodynamic model. And they found the frictional damping is the key to the nonlinear diffusive phenomena of hyperbolic waves.…”

mentioning

confidence: 99%

Global existence and asymptotic behavior of solutions to the nonisentropic bipolar hydrodynamic models

2011

Journal of Differential Equations

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In this paper, we consider a one-dimensional bipolar nonisentropic hydrodynamical model from semiconductor devices. This system takes the nonisentropic Euler-Poisson form with electric field and frictional damping added to the momentum equations. First, we prove global existence of smooth solutions to the Cauchy problem. Next, we also discuss the asymptotic behavior of the smooth solutions. We find that in large time, the densities of electron and hole tend to the same nonlinear diffusive wave, the momentums tend to the Darcy's law, and the temperatures tend to the ambient device temperature. Finally, we can obtain the algebraic decay rate of the densities to the same nonlinear diffusive wave, the momentums to the Darcy's law and the temperatures to the ambient device temperature, and the exponential decay of their difference and the electric field to zero. We can show our results by precise energy methods.

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Stability of planar diffusion wave for three‐dimensional bipolar Euler–Poisson system with time‐dependent over‐damping

Wu,

Hou

2024

Math Methods in App Sciences

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This paper is concerned with the asymptotic behavior of the solution to the Cauchy problem for the three‐dimensional bipolar Euler–Poisson system with time‐dependent over‐damping. We prove that the Cauchy problem admits a unique global‐in‐time smooth solution that tends to the planar diffusion wave as time goes to infinity provided that the initial perturbation is sufficiently small. Moreover, we also obtain the convergence rate of the solution toward the planar diffusion wave. The proof is completed by the time‐weighted energy method.

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Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors

Cited by 78 publications

References 28 publications

Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

Global existence and asymptotic behavior of solutions to the nonisentropic bipolar hydrodynamic models

Stability of planar diffusion wave for three‐dimensional bipolar Euler–Poisson system with time‐dependent over‐damping

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