In practical settings, the echo cancellation problem generally requires the adaptation of an IIR filter using some optimality criterion. This brings two problems: direct adaptation of numerator and denominator polynomial coefficients of IIR filters might result in unstable systems and/or the optimization might result in a suboptimal local minimum of the criterion. These two issues are addressed...

We study the dynamics of Kelvin waves along a quantum vortex filament in the presence of mutual friction and a driving fluid while taking into account non-local effects due to Biot–Savart integrals. The Schwarz model reduces to a nonlinear and nonlocal dynamical system of dimension three, the solutions of which determine the translational and rotational motion of the Kelvin waves, as well as th...

Purely gravitational perturbations are considered in a thin rotating disk composed of several gas and stellar components. The dispersion relation for the axisymmetric density waves propagating through the disk is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon (...

The stability of the Camassa-Holm (periodic) peakons in the dynamics of an integrable shallow-water-type system is investigated. A variational approach with the use of the Lyapunov method is presented to prove the variational characterization and the orbital stability of these wave patterns. In addition, a sufficient condition for the global existence of strong solutions is given. Finally, a lo...

This paper is devoted to studying a reaction-diffusion-chemotaxis model with a volume-filling effect in a bounded domain with Neumann boundary conditions. We first establish the global existence of classical solutions bounded uniformly in time. Then applying the asymptotic analysis and bifurcation theory, we obtain both the local and global structure of steady states bifurcating from the homoge...