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L ∞ variational problems for maps and the Aronsson PDE system
(Journal of Differential Equations, 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 ...
Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results
(Journal of Functional Analysis, 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 ...
Robust grid adaptation for efficient uncertainty quantification
(AIAA Journal, 2012-12-31)
In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used ...
Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
(Journal des Mathematiques Pures et Appliquees, 2012-12-31)
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrödinger equations on the real line. Recently, the authors have introduced viscous and ...
Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space
(Journal of Differential Equations, 2012-12-31)
We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u)=-∫ ℝdK(x,y)(u(y)-u(x))dy. Here we consider a kernel K(x, y)=ψ(y-a(x))+ψ(x-a(y)) where ψ is a bounded, nonnegative ...
Continuous adjoint approach for the spalart-allmaras model in aerodynamic optimization
(AIAA Journal, 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 ...
A result concerning the global approximate controllability of the Navier-Stokes system in dimension 3
(Journal des Mathematiques Pures et Appliquees, 2012-12-31)
In this paper we deal with the three-dimensional Navier-Stokes system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some ...
Local Exact Controllability for the One-Dimensional Compressible Navier-Stokes Equation
(Archive for Rational Mechanics and Analysis, 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 ...
Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces
(Journal of Mathematical Analysis and Applications, 2012-12-31)
In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with H 1(Ω) initial data, for a system of partial differential equations, which consists of the equations of linear elasticity ...
Non-reflecting boundary condition on ellipsoidal boundary
(Numerical Analysis and Applications, 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 ...