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On the regularity of null-controls of the linear 1-d heat equation [Sur la regularité des contrôles pour l'équation de la chaleur linéaire]
(2011-12-31)
The 1-d heat equation in a bounded interval is null-controllable from the boundary. More precisely, for each initial data y0εL2(0,1) there corresponds a unique boundary control of minimal L2(0,T)-norm which drives the state ...
Fine structure of spectral properties for random correlation matrices: An application to financial markets
Livan, G.; Alfarano, S.; Scalas, E.
(2011-12-31)
(2011-12-31)
We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded ...
Solutions to a model with Neumann boundary conditions for phase transitions driven by configurational forces
(2011-12-31)
We study an initial boundary value problem of a model describing the evolution in time of diffusive phase interfaces in solid materials, in which martensitic phase transformations driven by configurational forces take ...
Observability of heat processes by transmutation without geometric restrictions
(2011-12-31)
The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] ...
Hardy inequality and Pohozaev identity for operators with boundary singularities: Some applications
(2011-12-31)
We consider the Schrödinger operator Aλ:=-δ-λ/|x|2, λ∈R, when the singularity is located on the boundary of a smooth domain Ω⊂RN, N≥1.The aim of this Note is two folded. Firstly, we justify the extension of the classical ...
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems
(2011-12-31)
This work is concerned with (n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using ...
Dispersive Properties for Discrete Schrödinger Equations
(2011-12-31)
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting ...
Solvability via viscosity solutions for a model of phase transitions driven by configurational forces
(2011-12-31)
This article is concerned with an initial-boundary value problem for an elliptic-parabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model ...
The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide
(2011-12-31)
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 ...
Stationary policies for the second moment stability in a class of stochastic systems
(2011-12-31)
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 long-run average cost under a stationary policy is equivalent ...