Global existence of solutions for the nonlinear Boltzmann equation of semiconductor physics.

Autores: Francisco José Mustieles Moreno
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 6, Nº 1-2, 1990, págs. 43-60
Idioma: inglés
DOI: 10.4171/rmi/94
Títulos paralelos:
- Existencia global de soluciones para la ecuación no lineal de Boltzmann en física de semiconductores.
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Resumen
- 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.