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This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a…
The problem of kink stability of isothermal spherical self-similar flow in newtonian gravity is revisited. Using distribution theory we first develop a general formula of perturbations, linear or non-linear, which consists of three sets of…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued…
The Evans function is a tool for assessing the stability of travelling wave solutions for partial differential equations. A recent paper (math.NA/0605581) analyzes the order reduction experienced when evaluating the Evans function…
We develop a feedback control framework for stabilizing the McKean-Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or accelerate convergence to it using a time-dependent control…
We generalize the periodic Evans function approach recently used to study the spectral stability of Stokes wave and gravity-capillary (including Wilton ripples) in water of finite depth to study spectral stability of Stokes waves in water…
Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explicitly address the goal of driving a system into a…
This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…
This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…
We investigate the spectral instability of a $2\pi/\kappa$ periodic Stokes wave of sufficiently small amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests instability whenever the unperturbed wave is…
In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…
The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each of which the non-linear wave equation is homogeneous. In such…
We theoretically propose a new method in cavity- and surface-enhanced Raman spectroscopy (SERS) with improved temporal resolution in the measurement of stochastic Raman spectral fluctuations. Our approach combines Fourier spectroscopy and…