Related papers: Stable methods to solve the impedance matrix for r…
Impedance matrices are obtained for radially inhomogeneous structures using the Stroh-like system of six first order differential equations for the time harmonic displacement-traction 6-vector. Particular attention is paid to the newly…
A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time…
One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We…
We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low…
We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $\Lambda<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static…
This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et…
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
We consider pattern-forming fronts in the complex Ginzburg-Landau equation with a traveling spatial heterogeneity which destabilizes, or quenches, the trivial ground state while progressing through the domain. We consider the regime where…
The surface-impedance matrix method is used to study interfacial waves polarized in a plane of symmetry of anisotropic elastic materials. Although the corresponding Stroh polynomial is a quartic, it turns out to be analytically solvable in…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…