Global conservative solutions of the Camassa-Holm equation for initial data nonvanishing asymptotics [PDF]
Discrete Contin. Dyn. Syst. 32, 4209-4227 (2012), 2011 We study global conservative solutions of the Cauchy problem for the Camassa-Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.
arxiv +1 more source
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model [PDF]
, 2014 We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model.
Baudron, Anne-Marie A. -M. +4 more
core +5 more sources
A mathematical PDE perspective on the Chapman–Enskog expansion
, 2013 This paper presents in a synthetic way some recent advances on hydrodynamic limits of the Boltzmann equation. It aims at bringing a new light to these results by placing them in the more general framework of asymptotic expansions of Chapman–Enskog type ...
L. Saint-Raymond
semanticscholar +1 more source
The general peakon-antipeakon solution for the Camassa-Holm equation [PDF]
J. Hyper. Differential Equations 13, 353-380 (2016), 2015 We compute explicitly the peakon-antipeakon solution of the Camassa-Holm equation $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ in the non-symmetric and $\alpha$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.
arxiv +1 more source
Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation
, 2016 Extended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time ...
Zhicheng Hu, Ruo Li, Zhonghua Qiao
semanticscholar +1 more source
The Lorentz Process with a Nearly Periodic Distribution of Scatterers [PDF]
, 2022 We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with the periodic Lorentz gas, which does not satisfy the Boltzmann equation in the limit.
arxiv +1 more source
Rigorous derivation of a binary-ternary Boltzmann equation for a non ideal gas of hard spheres
Forum of Mathematics, SigmaThis paper focuses on dynamics of systems of particles that allow interactions beyond binary, and their behavior as the number of particles goes to infinity.
Ioakeim Ampatzoglou, Nataša Pavlović
doaj +1 more source
On the initial-boundary value problem for a Bingham fluid in a three-dimensional domain
, 1987 The initial-boundary value problem associated with the motion of a Bingham fluid is considered. The existence and uniqueness of strong solution is proved under a certain assumption on the data.
J. U. Kim
semanticscholar +1 more source
Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences
, 1997 The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of twistor theory,
Boyer +30 more
core +2 more sources
Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators [PDF]
, 2012 In many works, the linearized non-cutoff Boltzmann operator is considered to behave essentially as a fractional Laplacian. In the present work, we prove that the linearized non-cutoff Boltzmann operator with Maxwellian molecules is exactly equal to a ...
Chao-jiang Xu +6 more
core +5 more sources