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Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results
(2012-12-31)
The aim of this paper is two folded. Firstly, we study the validity of a Pohozaev-type identity for the Schrödinger operator A λ:=-δ-λ/|x| 2, λ∈R, in the situation where the origin is located on the boundary of a smooth ...
Local Exact Controllability for the One-Dimensional Compressible Navier-Stokes Equation
(2012-12-31)
In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions ...
L ∞ variational problems for maps and the Aronsson PDE system
(2012-12-31)
By employing Aronsson's absolute minimizers of L ∞ functionals, we prove that absolutely minimizing maps u:Rn→RN solve a "tangential" Aronsson PDE system. By following Sheffield and Smart (2012) [24], we derive δ ∞ with ...
Continuous adjoint approach for the spalart-allmaras model in aerodynamic optimization
(2012-12-31)
In this paper, the continuous adjoint method to compute shape sensitivities in aerodynamic design with turbulence modeling is described and developed. The focus is on compressible flows described by the Reynolds-averaged ...
Inverse problem for the heat equation and the Schrödinger equation on a tree
(2012-12-31)
In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a star-shaped tree. The Carleman ...
Shallow-shell models by Γ-convergence
(2012-12-31)
In this paper we derive, by means of Γ-convergence, the shallow-shell models starting from non-linear three-dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization ...
The near-extreme density of intraday log-returns
(2012-12-31)
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 non-stationarity and dependence between ...
Non-reflecting boundary condition on ellipsoidal boundary
(2012-12-31)
The modeling of wave propagation problems using finite element methods usually requires the truncation of the computation domain around the scatterer of interest. Absorbing boundary conditions are classically considered ...
Existence of a global weak solution to Compressible Primitive Equations
(2012-12-31)
In this Note, we show a global weak existence result for a two dimensional Compressible Primitive Equations for atmosphere dynamics modeling.
The wave equation: Control and numerics
(2012-12-31)
In these Notes we make a self-contained 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 ...