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

Revista Matemática Iberoamericana (1990)

- Volume: 6, Issue: 1-2, page 43-59
- ISSN: 0213-2230

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topMustieles, 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 -

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