A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the systemwith independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics fromheterogeneous and homogeneous exponential samples in the sense of t...

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L ∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

In this article we illustrate a new method to extend local wellposedness results for dispersive equations to global ones. The main ingredient of this method is the definition of a family of what we call almost conservation laws. In particular we analyze the Korteweg-de Vries initial value problem and we illustrate in general terms how the “algorithm” that we use to formally generate almost cons...

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating ...

We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the gravitational two body problem.