Related papers: A new stochastic differential equation approach fo…
We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can…
We construct unique martingale solutions to the damped stochastic wave equation $$ \mu \frac{\partial^2u}{\partial t^2}(t,x)=\Delta u(t,x)-\frac{\partial u}{\partial t}(t,x)+b(t,x,u(t,x))+\sigma(t,x,u(t,x))\frac{dW_t}{dt},$$ where $\Delta$…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…
We are interested in the localization of defects in non-absorbing inhomogeneous media with far-field measurements generated by plane waves. In localization problems, most so-called sampling methods are based on a characterization involving…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient…
We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0,T] x \partial \Omega, where \Omega\subset\R^3 is some bounded…
This paper investigates the parabolic scaling limit of a damped stochastic wave map from the real line into the two-dimensional sphere, perturbed by multiplicative Gaussian noise of co-normal type. We prove that under this rescaling, the…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applications such as networked control systems. Sufficient and necessary conditions are obtained…
Processes which arise as solutions to stochastic differential equations involving the local time (SDELTs), such as skew Brownian motion, are frequent sources of inspiration in theory and applications. Existence and uniqueness results for…
The traditional wave equation models wave propagation in an ideal conducting medium. For characterizing the wave propagation in inhomogeneous media with frequency dependent power-law attenuation, the space-time fractional wave equation…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck…