On the Multidimensional Bipolar Isothermal Quantum Drift-Diffusion Model

Jian Wei Dong

doi:10.4028/www.scientific.net/AMR.466-467.186

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 466-467On the Multidimensional Bipolar Isothermal Quantum...

On the Multidimensional Bipolar Isothermal Quantum Drift-Diffusion Model

Abstract:

The bipolar isothermal quantum drift-diffusion model in two or three space dimensions with initial value and periodic boundary conditions is investigated. The global existence of weak solution to the problem is obtained by using semi-discretizing in time and entropy estimate. Furthermore, it is shown that the solution to the problem exponentially approaches its mean value as time increases to infinity by using a series of inequality technique.

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Periodical:

Advanced Materials Research (Volumes 466-467)

Pages:

186-190

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.466-467.186

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Online since:

February 2012

Authors:

Jian Wei Dong

Keywords:

Existence, Long-Time Behavior, Quantum Drift-Diffusion Model, Weak Solution

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References

[1] A. Jungel. Nonlinear problems in quantum semiconductor modeling,. Nonlinear Analysis, vol. 47 ( 2001), P. 5873-5884.

Google Scholar

[2] L. Chen, Q. Ju. Existence of solution and semiclassical limit for quantum driftdiffusion model. Z. Angew. Math. Phys., vol. 58 (2007), P. 1-15.

Google Scholar

[3] A. Jungel, I. Violet. The quasineutral limit in the quantum drift-diffusion equations. Asympt. Anal., vol. 53 (2007), P. 139-157.

Google Scholar

[4] X. Chen, L. Chen, H. Jian. The Dirichlet problem of the quantum drift-diffusion model. Nonlinear Analysis, vol. 69 (2008), P. 3084-3092.

DOI: 10.1016/j.na.2007.09.003

Google Scholar

[5] X. Chen, L. Chen, H. Jian. Existence, semiclassical limit and long-time behavior of solution to quantum drift-diffusion model. Nonlinear Analysis: Real World Applications, vol. 10 (2009), P. 1321-1342.

DOI: 10.1016/j.nonrwa.2008.01.008

Google Scholar

[6] X. Chen. The global existence and semiclassical limit of weak solutions to multidimensional quantum drift-diffusion model. Advanced Nonlinear Studies, vol. 7 (2007), P. 651-670.

DOI: 10.1515/ans-2007-0408

Google Scholar

[7] A. Jungel, D. Matthes. The Derrida-Lebowitz-Speer-Spohn equation: existence, nonuniqueness, and decay rates of the solutions. SIAM J. Math. Anal., vol. 39 (2008), P. 1996-(2015).

DOI: 10.1137/060676878

Google Scholar