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Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
(2012-12-31)
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and ...
Robust grid adaptation for efficient uncertainty quantification
(2012-12-31)
In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used ...
Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results
(2012-12-31)
The aim of this paper is two folded. Firstly, we study the validity of a Pohozaev-type identity for the Schrödinger operator A λ:=-δ-λ/|x| 2, λ∈R, in the situation where the origin is located on the boundary of a smooth ...
Local Exact Controllability for the One-Dimensional Compressible Navier-Stokes Equation
(2012-12-31)
In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions ...
A result concerning the global approximate controllability of the Navier-Stokes system in dimension 3
(2012-12-31)
In this paper we deal with the three-dimensional Navier-Stokes system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some ...
The wave equation: Control and numerics
(2012-12-31)
In these Notes we make a self-contained presentation of the theory that has been developed recently for the numerical analysis of the controllability properties of wave propagation phenomena and, in particular, for the ...
On the non-stationarity of financial time series: Impact on optimal portfolio selection
Livan, G.; Inoue, J.-I.; Scalas, E.
(2012-12-31)
(2012-12-31)
We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence ...
Shallow-shell models by Γ-convergence
(2012-12-31)
In this paper we derive, by means of Γ-convergence, the shallow-shell models starting from non-linear three-dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization ...
The near-extreme density of intraday log-returns
(2012-12-31)
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between ...
Classical non-mass-preserving solutions of coagulation equations
(2012-12-31)
In this paper we construct classical solutions of a family of coagulation equations with homogeneous kernels that exhibit the behaviour known as gelation. This behaviour consists in the loss of mass due to the fact that ...