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Numerical approximation of a one-dimensional elliptic optimal design problem
(2011-12-31)
We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, ...
On a nonlocal moving frame approximation of traveling waves
(2011-12-31)
The profiles of traveling wave solutions of a 1-d reaction-diffusion parabolic equation are transformed into equilibria of a nonlocal equation, by means of an appropriate nonlocal change of variables. In this new formulation ...
Switching control
(2011-12-31)
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 ...
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 ...
Semi-markov graph dynamics
Raberto, M.; Rapallo, F.; Scalas, E.
(2011-12-31)
(2011-12-31)
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of ...
Counter-examples of regularity behavior for σ-evolution equations
(2011-12-31)
In this paper, we mainly discuss the infinite loss of regularity and μ-loss for a σ-evolution type model with oscillating in time coefficients. On the one hand, an explicit counter-example has been constructed in the ...
Explicit singular viscosity solutions of the Aronsson equation
(2011-12-31)
We establish that when n≥2 and H∈C1(Rn) is a Hamiltonian such that some level set contains a line segment, the Aronsson equation D2u:Hp(Du)⊗Hp(Du)=0 admits explicit entire viscosity solutions. They are superpositions of a ...
High frequency wave packets for the Schrödinger equation and its numerical approximations [Paquets d'ondes à haute fréquence pour l'équation de Schrödinger et ses approximations numériques]
(2011-12-31)
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in ...