For a rescaled linear one-dimensional transport equation with spatial dependence describing the evolution of the electron distribution in a weakly ionized host medium under the influence of a constant electric field, we derive recursively the n-th term in the Hilbert expansion and prove that the n-th order Hilbert expansion provides an (n + 1)-th order approximation of the electron distribution function and the drift velocity under certain initial conditions. The proof is based on the perturbation formula for the mild solution of the initial-value problem and an existence result for stationary solutions in a weighted L1-space.
Asymptotic behaviour of drift velocity with spatial diffusion of electrons / G. FROSALI; C. VAN DER MEE. - In: TRANSPORT THEORY AND STATISTICAL PHYSICS. - ISSN 0041-1450. - STAMPA. - 24(1-3):(1995), pp. 241-262. [10.1080/00411459508205128]
Asymptotic behaviour of drift velocity with spatial diffusion of electrons
FROSALI, GIOVANNI;
1995
Abstract
For a rescaled linear one-dimensional transport equation with spatial dependence describing the evolution of the electron distribution in a weakly ionized host medium under the influence of a constant electric field, we derive recursively the n-th term in the Hilbert expansion and prove that the n-th order Hilbert expansion provides an (n + 1)-th order approximation of the electron distribution function and the drift velocity under certain initial conditions. The proof is based on the perturbation formula for the mild solution of the initial-value problem and an existence result for stationary solutions in a weighted L1-space.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.