Stochastic approximations of the solution of a full Boltzmann equation with small initial data
Sylvie Meleard (1998)
ESAIM: Probability and Statistics
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Sylvie Meleard (1998)
ESAIM: Probability and Statistics
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Dario Benedetto, Mario Pulvirenti (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
Pierre Del Moral, Nicolas G. Hadjiconstantinou (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This special volume of the ESAIM Journal, , contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide...
Hélène Guérin (2010)
ESAIM: Probability and Statistics
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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given....
Fournier, Nicolas (2006)
Electronic Communications in Probability [electronic only]
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Hélène Guérin (2004)
ESAIM: Probability and Statistics
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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given....
S. K. Srinivasan, R. Vasudevan (1969)
Annales de l'I.H.P. Physique théorique
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