Browsing Past Topics (PT) by Title
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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 ... 
TimeDependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
(20131231)In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. We will suppose the coefficients to be logZygmund continuous in time and ... 
Topological degree in the generalized gause preypredator model
(20141231)We consider a generalized Gause preypredator model with Tperiodic continuous coefficients. In the case where the Poincar√© map P over time T is well defined, the result of the paper can be explained as follows: we locate ... 
Transmutation techniques and observability for timediscrete approximation schemes of conservative systems
(20141231)In this article, we consider abstract linear conservative systems and their timediscrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the ... 
Traveling waves to models of solidsolid phase transitions driven by configurational forces
(20111231)We study the existence of traveling/standing waves to models based on configurational forces. These models describe, respectively, structural phase transitions in solids, e.g., Shape memory alloys, and phase transitions ... 
Uniformly exponentially stable approximations for a class of damped systems
(20091231)We consider time semidiscrete approximations of a class of exponentially stable infinitedimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semidiscrete systems, due ... 
Unsteady mixed flows in non uniform closed water pipes: a Full Kinetic Approach
(20141231)We recall the Pressurized and Free Surface model constructed for the modeling of unsteady mixed flows in closed water pipes where transition points between the free surface and pressurized flow are treated as a free boundary ... 
Weak observability estimates for 1D wave equations with rough coefficients
(20141231)In this paper we prove observability estimates for 1dimensional wave equations with nonLipschitz coefficients. For coefficients in the Zygmund class we prove a "classical" estimate, which extends the wellknown observability ... 
Wellposedness in critical spaces for the system of compressible NavierStokes in larger spaces
(20111231)This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≥2. We address the question of wellposedness for large data having critical Besov regularity. Our result improves the analysis ...