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Propagation of 1D Waves in Regular Discrete Heterogeneous Media: A Wigner Measure Approach
(2014-12-31)
In this article, we describe the propagation properties of the one-dimensional wave and transport equations with variable coefficients semi-discretized in space by finite difference schemes on non-uniform meshes obtained ...
Averaged control
(2014-12-31)
We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First ...
The behavior of domain decomposition methods when the overlapping length is large
(2014-12-31)
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm ...
Derivation of a homogenized von-Kármán shell theory from 3D elasticity
(2014-12-31)
We derive homogenized von Kármán shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the period of oscillation $\epsilon$ of the material ...
The turnpike property infinite-dimensional nonlinear optimal control
(2014-12-31)
Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given ...
Transmutation techniques and observability for time-discrete approximation schemes of conservative systems
(2014-12-31)
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the ...
Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
(2014-12-31)
In the present article we consider several issues concerning the doubly parabolic Keller-Segel system (1.1)-(1.2) in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, ...
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
(2014-12-31)
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ...
On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons
(2014-12-31)
In this paper we prove that the solutions of the isotropic, spatially homogeneous Nordheim equation for bosons with bounded initial data blow up in finite time in the L‚àû norm if the values of the energy and particle ...
Recovery of an initial temperature from discrete sampling
(2014-12-31)
The problem of recovering the initial temperature of a body from discrete temperature measurements made at later times is studied. While this problem has a general formulation, the results of this paper are only given in ...