On systems of conservation laws with fluxes that are entropies.
On a Cahn–Hilliard model for phase separation with elastic misfit
On a class of discrete generation interacting particle systems.
On a class of nonlinear integral equations arising in neutron transport.
On a kinetic model of the internet traffic.
On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature
On a variant of Korn’s inequality arising in statistical mechanics
We state and prove a Korn-like inequality for a vector field in a bounded open set of , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are...
On a variant of Korn's inequality arising in statistical mechanics
We state and prove a Korn-like inequality for a vector field in a bounded open set of , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case...
On bilinear kinetic equations. Between micro and macro descriptions of biological populations
In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...
On chaotic dynamics in rational polygonal billiards.
On classical solutions of the relativistic Vlasov-Klein-Gordon system.
On conservative and entropic discrete axisymmetric Fokker-Planck operators
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with...
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments...
On global smooth solutions to the 3D Vlasov–Nordström system
On global solutions for the Vlasov-Poisson system.
On local smooth solutions for the Vlasov equation with the potential of interactions .
On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
On Prigogine's approaches to irreversibility: a case study by the baker map.
On regularized solution for BBGKY hierarchy of one-dimensional infinite system.