Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.

Mustieles, Francisco José. "Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.." Revista Matemática Iberoamericana 6.1-2 (1990): 43-59. <http://eudml.org/doc/39395>.

@article{Mustieles1990,
abstract = {In this paper we give a proof of the existence and uniqueness of smooth solutions for the nonlinear semiconductor Boltzmann equation. The method used allows to obtain global existence in time and uniqueness for dimensions 1 and 2. For dimension 3 we can only assure local existence in time and uniqueness. First, we define a sequence of solutions for a linearized equation and then, we prove the strong convergence of the sequence in a suitable space. The metod relies on the use of interpolation estimates in order to control the decay of the solution when the wave vector goes to infinity.},
author = {Mustieles, Francisco José},
journal = {Revista Matemática Iberoamericana},
keywords = {Semiconductores; Ecuaciones diferenciales en derivadas parciales; Alineal; Teorema de existencia; Soluciones; Boltzmann equation; semiconductors; Vlasov-Fokker-Planck equation; nonlinear integral operators; global existence; local existence; uniqueness},
language = {eng},
number = {1-2},
pages = {43-59},
title = {Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.},
url = {http://eudml.org/doc/39395},
volume = {6},
year = {1990},
}

TY - JOUR
AU - Mustieles, Francisco José
TI - Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.
JO - Revista Matemática Iberoamericana
PY - 1990
VL - 6
IS - 1-2
SP - 43
EP - 59
AB - In this paper we give a proof of the existence and uniqueness of smooth solutions for the nonlinear semiconductor Boltzmann equation. The method used allows to obtain global existence in time and uniqueness for dimensions 1 and 2. For dimension 3 we can only assure local existence in time and uniqueness. First, we define a sequence of solutions for a linearized equation and then, we prove the strong convergence of the sequence in a suitable space. The metod relies on the use of interpolation estimates in order to control the decay of the solution when the wave vector goes to infinity.
LA - eng
KW - Semiconductores; Ecuaciones diferenciales en derivadas parciales; Alineal; Teorema de existencia; Soluciones; Boltzmann equation; semiconductors; Vlasov-Fokker-Planck equation; nonlinear integral operators; global existence; local existence; uniqueness
UR - http://eudml.org/doc/39395
ER -