Browsing Past Topics (PT) by Title
Now showing items 193212 of 220

Spike controls for elliptic and parabolic PDEs
(20131231)We analyze the use of measures of the minimal norm to control elliptic and parabolic equations. We prove the sparsity of the optimal control. In the parabolic case, we prove that the solution of the optimization problem ... 
A splitting method for the augmented Burgers equation
(20170701)In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of ﬁrst order. We also analyze the largetime behavior of the approximated solution by obtaining the ﬁrst term in the ... 
Stabilization of the wave equation on 1D networks
(20091231)In this paper we study the stabilization of the wa ve equation on general 1d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. ... 
Stationary policies for the second moment stability in a class of stochastic systems
(20111231)This paper presents a study on the uniform second moment stability for a class of stochastic control system. The main result states that the existence of the longrun average cost under a stationary policy is equivalent ... 
Stationary waves to viscous heatconductive gases in halfspace: Existence, stability and convergence rate
(20101231)The main concern of this paper is to study largetime behavior of solutions to an ideal polytropic model of compressible viscous gases in onedimensional halfspace. We consider an outflow problem and obtain a convergence ... 
Statistical analysis and agentbased microstructure modeling of highfrequency financial trading
(20121231)A simulation of highfrequency market data is performed with the Genoa Artificial Stock Market. Heterogeneous agents trade a risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market ... 
Strichartz estimates for the Schrödinger equation on a tree and applications
(20101231)In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We obtain Strichartzlike estimates for the linear semigroup and apply them to ... 
Switching control
(20111231)We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to another in a systematic way so that, at ... 
Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control
(20141231)This work describes the propagation properties of the socalled symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1d wave equation. This is done by means of linear approximations on uniform ... 
The asymptotic behaviour of the heat equation in a twisted DirichletNeumann waveguide
(20111231)We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay ... 
The behavior of domain decomposition methods when the overlapping length is large
(20141231)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 ... 
The Hardy inequality and the heat equation in twisted tubes
(20101231)We show that a twist of a threedimensional tube of uniform crosssection yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for ... 
The L∞null controllability of parabolic equation with equivalued surface boundary conditions
(20131231)In this paper, we obtain the L∞null controllability of the parabolic equation with equivalued surface boundary conditions in Ω×[0,T]. The control is supported in the product of an open subset of Ω and a subset of [0,T] ... 
The nearextreme density of intraday logreturns
(20121231)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 nonstationarity and dependence between ... 
The subelliptic ∞Laplace system on CarnotCarathéodory spaces
(20131231)Given a CarnotCarathéodory space Ω ⊆ ℝn with associated frame of vector fields X = {X<inf>1</inf>,⋯, X<inf>m</inf>}, we derive the subelliptic ∞Laplace system for mappings u: Ω → ℝN, which reads δX∞u:=(Xu ⊗ Xu + 
The turnpike property infinitedimensional nonlinear optimal control
(20141231)Turnpike properties have been established long time ago in finitedimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given ... 
The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks
(20131231)In this article we study, by the vanishing viscosity method, the sensitivity analysis of an optimal control problem for 1D scalar conservation laws in the presence of shocks. It is reduced to investigate the vanishing ... 
The wave equation: Control and numerics
(20121231)In these Notes we make a selfcontained 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 ... 
Time asymptotics for a critical case in fragmentation and growthfragmentation equations
(20160101)Fragmentation and growthfragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the longtime asymptotics of two critical cases of these equations, ... 
Time discrete wave equations: Boundary observability and control
(20091231)In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable ...