The Child–Langmuir Law for the Boltzmann Equation of Semiconductors
Naoufel Ben Abdallah, Pierre Degond · SIAM Journal on Mathematical Analysis · 1995
We investigate the so-called Child-Langmuir asymptotics of the one-dimensional stationary Boltzmann-Poisson system. The asymptotics apply when the lattice temperature is small and leads to a singular perturbation problem. We derive the limit problem associated with these asymptotics, and prove the existence of the Child-Langmuir current.