TY - JOUR
T1 - Stationary Quantum BGK Model for Bosons and Fermions in a Bounded Interval
AU - Bae, Gi Chan
AU - Yun, Seok Bae
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - In this paper, we consider the existence problem for a stationary relaxational models of the quantum Boltzmann equation. More precisely, we establish the existence of mild solution to the fermionic or bosonic quantum BGK model in a slab with inflow boundary data. Unlike the classical case, it is necessary to verify that the quantum local equilibrium state is well-defined, and the transition from the non-condensed state to the condensated state (bosons), or from the non-saturated state to the saturated state (fermions) does not arise in our solution space.
AB - In this paper, we consider the existence problem for a stationary relaxational models of the quantum Boltzmann equation. More precisely, we establish the existence of mild solution to the fermionic or bosonic quantum BGK model in a slab with inflow boundary data. Unlike the classical case, it is necessary to verify that the quantum local equilibrium state is well-defined, and the transition from the non-condensed state to the condensated state (bosons), or from the non-saturated state to the saturated state (fermions) does not arise in our solution space.
KW - Inflow boundary conditions
KW - Quantum BGK model
KW - Quantum Boltzmann equation
KW - Relaxation time approximation
KW - Stationary problems
UR - https://www.scopus.com/pages/publications/85077044026
U2 - 10.1007/s10955-019-02466-2
DO - 10.1007/s10955-019-02466-2
M3 - Article
AN - SCOPUS:85077044026
SN - 0022-4715
VL - 178
SP - 845
EP - 868
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 4
ER -