Abstract. We develop a general theory of the swelling kinetics of polymer gels, with the view that a polymer gel is a two-phase fluid. The model we propose is a free boundary problem and can be used to understand both contraction and swelling, including complete dissolving or dehydration of polymeric gels. We show that the equations of motion satisfy a minimum energy dissipation rate principle ...

We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time, and a finite element discretization in space. The key ingredient of the new algorithm is a block Jacobi smoother. We present a detailed convergence analysis when the algorithm is applied to the heat equation, and...

Keywords: Delay dynamic equations Fixed point theory Lyapunov Periodic solutions Stability Time scales a b s t r a c t Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x ∆ (t) = −a(t)x(δ(t))δ ∆ (t). Moreo...

The aim of this paper is two-fold. First we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple target tracking context. We study its stability properties, characterize its long time behavior and provide a series of weak Lipschitz type functional contraction inequalities. Second we design and analyze an original particle scheme to approximate nu...

Abstract. The concern of this paper is the derivation and the analysis of a simple explicit numerical scheme for general one-dimensional filtration equations. It is based on an alternative formulation of the problem using the pseudo-inverse of the density’s repartition function. In particular, the numerical approximations can be proven to satisfy a contraction property for a Wasserstein metric....

Direction finding techniques are usually based on the 2ndorder statistics of the received data. In this paper, we propose a MUSIC-like direction finding algorithm which uses a matrix-valued statistic based on the contraction of the 4thorder cumulant tensor of the array data (4-2 MUSIC). We then derive, in a unified framework, the asymptotic covariance of estimation errors for both 2nd-order and...

For the Vlasov-Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei, J. Stat. Phys., 92:301-323, 1998) depends smoothly on the random variable if the time asymptotic profile does, under the smoothness and smallness assumptions similar to the deterministic case. The main idea is to generalize th...

We analyze an equation governing the motion of an interface between two fluids in a pressure field. In two dimensions, the interface is described by a conformal mapping which is analytic in the exterior of the unit disc. This mapping obeys a nonlocal nonlinear equation. When there is no pumping at infinity, there is conservation of area and contraction of the length of the interface. We prove g...

This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the...