Geodesic
Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
Applications of Mathematics, Tome 69 (2024) no. 1, pp. 113-137

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in $\mathbb {R}^3$, we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively.
DOI : 10.21136/AM.2023.0039-23
Classification : 35B40, 35Q40, 76Y05, 82D37
Keywords: quantum hydrodynamic equation; quantum Euler-Poisson system; bipolar semiconductor model; relaxation-time limit 
@article{10_21136_AM_2023_0039_23,
     author = {Ra, Sungjin and Hong, Hakho},
     title = {Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors},
     journal = {Applications of Mathematics},
     pages = {113--137},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2024},
     doi = {10.21136/AM.2023.0039-23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0039-23/}
}
TY  - JOUR
AU  - Ra, Sungjin
AU  - Hong, Hakho
TI  - Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
JO  - Applications of Mathematics
PY  - 2024
SP  - 113
EP  - 137
VL  - 69
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0039-23/
DO  - 10.21136/AM.2023.0039-23
LA  - en
ID  - 10_21136_AM_2023_0039_23
ER  - 
%0 Journal Article
%A Ra, Sungjin
%A Hong, Hakho
%T Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
%J Applications of Mathematics
%D 2024
%P 113-137
%V 69
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0039-23/
%R 10.21136/AM.2023.0039-23
%G en
%F 10_21136_AM_2023_0039_23
Ra, Sungjin; Hong, Hakho. Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors. Applications of Mathematics, Tome 69 (2024) no. 1, pp. 113-137. doi: 10.21136/AM.2023.0039-23

Cité par Sources :