Keywords
kinetic theory
fixed point
Ecuación de Boltzmann
teoría cinética
punto fijo
How to Cite
Abstract
An existence theorem for the Boltzmann Equation with force term and small initial data is proved in an L1 setting.
References
Bellomo, N.; Toscani, G. (1985) “On the Cauchy problem for the non-linear Boltzmann equation. Global existence, uniqueness and asymptotic stability”, Journal of Mathematical Physics 26(2): 334–338.
Bellomo, N.; Lachowicz, M. (1988) “On the asymptotic equivalence between the Enskog and the Boltzmann equations”, Journal of Statistical Physics 51(1–2): 233–247.
Bellomo, N.; Palczewski, A.; Toscani, G. (1988) Mathematical Topics in Nonlinear Kinetic Theory. World Scientific, Singapore.
Cercignani, C. (1988) “Small data existence for the Enskog equations in L1, Journal of Statistical Physics 51(1–2): 291–297.
Galeano, R.; Pérez, H. (2003) “Problema de Cauchy para la ecuación de Enskog no lineal con término fuerza” Foro-Red-Mat,UNAM-Mexico, vol(013).
Galeano, R.; Orozco, B.; Vásquez, M.O.; (2007) “Ecuación relativ́ıstica de Boltzman cerca al vacío”, Boletín de Matemática Sociedad Cubana de Matemáticas y Computación 5: 53–61.
Glassey, R. (1996) The Cauchy Problem in Kinetic Theory. SIAM, Philadelphia PA.
Hamdache, K. (1984) “Quelques résultats pour l’equation de Boltzmann”, C.R Acad. Science,Paris, série 1, 299(10): 431–434.
Illner, R.; Shinbrot, M. (1984) “The Boltzmann equation: global existence for a rare gas in a infinite vacuum”, Comm. math. Phys. 95(2):217–226.
Maslova, N.B. (1993) Nonlinear Evolution Equations: Kinetic Approach. World Scientific, Singapore.