Results 31 to 40 of about 667 (82)
, 1983 The two-dimensional free boundary problem for incompressible irrotational water waves without surface tension is proved to have exactly eight nontrivial conservation laws. Included is a discussion of what constitutes a conservation law for a general free
P. Olver
semanticscholar +1 more source
The Boltzmann-Grad asymptotic behavior of collisional dynamics: a brief survey [PDF]
Reviews in Mathematical Physics, 33 (2021) 2130001 (32 pages), 2020 The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.
arxiv +1 more source
Remarks on the stability of shock profiles for conservation laws with dissipation
, 1985 Two remarks are made. The first is to establish the stability of monotone shock profiles of the KdV-Burgers equation, based on an energy method of Goodman.
R. Pego
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Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation [PDF]
, 2012 In this paper, we consider a class of spatially homogeneous Boltzmann equation without angular cutoff.
Glangetas, Léo, Najeme, Mohamed
core +3 more sources
A Note on the Elliptic Sine-Gordon Equation
, 2003 The elliptic sine-Gordon equation originates from the static case of the hyperbolic sine-Gordon equation modeling the Josephson junction in superconductivity.
Goong Chen +4 more
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Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations
, 2014 In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems.
Gerasimenko, V. I.
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, 1989 In this paper we derive some results for the Zakharov-Shabat system of the form dm/dx = z2[J, m] + (zQ + P)m; J is diagonal and skewHermitian [8, 10, 12]. Following the idea of R. Beals and R. R.
Jyh-Hao Lee
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Kac's Process with Hard Potentials and a Moderate Angular Singularity [PDF]
, 2020 We investigate Kac's many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate independent of the number of particles $N$.
arxiv +1 more source
Cauchy problem for the Boltzmann-BGK model near a global Maxwellian
, 2010 In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the ...
Cercignani C. +4 more
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Network-based kinetic models: Emergence of a statistical description of the graph topology
European Journal of Applied MathematicsIn this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems.
Marco Nurisso +2 more
doaj +1 more source