## Search

Now showing items 31-40 of 69

#### Sensitivity analysis of 1-d steady forced scalar conservation laws

(2013-12-31)

We analyze 1 - d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t→ ∞ of the corresponding solutions of the scalar evolutionary hyperbolic conservation ...

#### Optimal Observation of the One-dimensional Wave Equation

(2013-12-31)

In this paper, we consider the homogeneous one-dimensional wave equation on [0,π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0,π]. Let L∈(0,1). We investigate the problem of maximizing ...

#### Blowup for a time-oscillating nonlinear heat equation

(2013-12-31)

In this paper, we study a nonlinear heat equation with a periodic time oscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according ...

#### Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations

(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 ...

#### Robust grid adaptation for efficient uncertainty quantification

(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 ...

#### 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 ...

#### Null controllability of viscous Hamilton-Jacobi equations

(2012-12-31)

We study the problem of null controllability for viscous Hamilton-Jacobi equations in bounded domains of the Euclidean space in any space dimension and with controls localized in an arbitrary open nonempty subset of the ...

#### 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 ...

#### Approximating travelling waves by equilibria of non-local equations

(2012-12-31)

We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution ...

#### On the quadratic finite element approximation of one-dimensional waves: Propagation, observation, and control

(2012-12-31)

We study the propagation, observation, and control properties of the quadratic P 2-classical finite element semidiscretization of the one-dimensional wave equation on a bounded interval. A careful Fourier analysis of the ...