This paper considers a boundary feedback control problem for a MIMO counter-propagating Raman amplifier. The system is modeled as a set of coupled semilinear hyperbolic partial differential equations with Lotka-Volterra type nonlinearity. The system is linearized about the steady-state solution, and a boundary controller is designed based on a Lyapunov functional whose time derivative is made s...

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: ∂u ∂t = J ∗ u− u+ f(x, u) t ∈ R, x ∈ R , where J is a probability density and f is a KPP nonlinearity periodic in the xvariables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the 0 state by an heterogeneous state. We also give a ...

Linear congruential pseudorandom numbers show several undesirable regularities which can render them useless for certain stochastic simulations. This was the motivation for important recent developments in nonlinear congruential methods for generating uniform pseudorandom numbers. It is particularly promising to achieve nonlinearity by employing the operation of multiplicative inversion with re...

In this article, we consider a stochastic PDE of parabolic type, driven by a space-time white-noise, and its numerical discretization in time with a semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded, then a dissipativity assumption is satisfied, which ensures that the SDPE admits a unique invariant probability measure, which is ergodic and strongly mixing with exponenti...

Abstract. In this paper we study the existence assertion of the initial boundary value problem for the equation ∂u ∂t = ∆e−∆u. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow “c...

In any dimension n ≥ 3, we show that spherically symmetric bounded energy solutions of the defocusing energy-critical nonlinear Schrödinger equation iut + ∆u = |u| 4 n−2 u in R × Rn exist globally and scatter to free solutions; this generalizes the three and four-dimensional results of Bourgain, 1999a and 1999b, and Grillakis, 2000. Furthermore we have bounds on various spacetime norms of the s...

A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis-Menten type modeling of the branching process. For branching rates large enough compared to capping rates, the exi...

Feedback control for the monodomain equations is studied. The dynamics of interest are governed by a coupled PDE-ODE reaction diffusion system with non-monotone nonlinearity of FitzHugh-Nagumo type. A localized distributed control is used to locally stabilize the nonlinear system. This is achieved by a Riccati-based feedback law, determined by the linearized system. It is shown that the Riccati...

A numerical method for estimating the nonlinear characterist ics of a coupling connecting two canti lever beams is presented in this paper. Nonlinearity representation of the coupling was assumed. The parametric values were determined by optimum matching the numerical solution of system response with experimental measurement. Pseudo mode shape was introduced to transform the governing motion eq...

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...