Related papers: Fourier series and sidewise profile control of 1-d…
We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path at the other free end. This sidewise…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
By mean of generalized Fourier series and Parseval's equality in weighted $L^{2}$--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp…
In this paper, we deal with the boundary controllability and boundary stabilizability of the 1D wave equation in non-cylindrical domain of the form ($\alpha (t)<x<\beta (t)$). By using the characteristics method, we prove under a natural…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…
We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…
In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in a one-dimensional wave equation in domains with a moving boundary. Some controls act…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…
We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…
In this article, we investigate certain theoretical aspects of the hierarchical controllability problem in one-dimensional wave equations within a moving domain using Stackelberg strategy. The controls are applied along a portion of the…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular…
In this paper, we study the simultaneous controllability of wave systems in an open domain of R d , d $\in$ N *. We obtain a partial controllability result on a co-finite dimensional space for wave equations coupled by a single control…
We study the tracking or sidewise controllability of the heat equation. More precisely, we seek for controls that, acting on part of the boundary of the domain where the heat process evolves, aim to assure that the normal trace or flux on…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
For a Legendre-Galerkin semi-discretization of the 1-D homogeneous wave equation, the high frequency components of the numerical solution prevent us from obtaining the boundary observability (inequality), uniformly with regard to the…
This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cindea-Munch, Controllability of the linear…
The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which…