Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Small data existence for the Boltzmann equation in L1*
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Keywords

Boltzmann equation
kinetic theory
fixed point
Ecuación de Boltzmann
teoría cinética
punto fijo

How to Cite

Galeano Andrades, R., Ortega Palencia, P., & Vásquez Ávila, M. O. (2012). Small data existence for the Boltzmann equation in L1*. Revista De Matemática: Teoría Y Aplicaciones, 19(1), 79–87. https://doi.org/10.15517/rmta.v19i1.2106

Abstract

An existence theorem for the Boltzmann Equation with force term and small initial data is proved in an L1 setting.

https://doi.org/10.15517/rmta.v19i1.2106
PDF (Español (España))

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.

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