Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice.
Exactness of skew products with expanding fibre maps
We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks.
Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.
Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.
Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations.
Existence of ground state configurations.
Existence of multi-dimensional infinite volume self-organized critical forest-fire models.
Existence of solutions for a model of self-gravitating particles with external potential
We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.
Existence theorems for the initial value problem for the Bogolyubov chain of equations in the space of sequences of bounded functions.
Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process
We study a free energy computation procedure, introduced in [Darve and Pohorille, J. Chem. Phys.115 (2001) 9169–9183; Hénin and Chipot, J. Chem. Phys.121 (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre et al., Nonlinearity21 (2008) 1155–1181],...
Existence, uniqueness and stability for spatially inhomogeneous Becker-Döring equations with diffusion and convection terms
We consider the spatially inhomogeneous Bekker-Döring infinite-dimensional kinetic system describing the evolution of coagulating and fragmenting particles under the influence of convection and diffusion. The simultaneous consideration of opposite coagulating and fragmenting processes causes many additional difficulties in the investigation of spatially inhomogeneous problems, where the space variable changes differently for distinct particle sizes. To overcome these difficulties, we use a modified...
Exponential waiting time for filling a large interval in the symmetric simple exclusion process