相关论文: Boundary Stabilization of the linear MGT equation …
The present work is devoted to the problem of boundary stabilization of the semilinear 1-D heat equation with nonlocal boundary conditions. The stabilizing controller is finite-dimensional, linear, given in an explicit form, involving only…
This paper addresses the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes the form of a either Dirichlet or Neumann trace. The output delay can be arbitrarily…
In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust…
We present the new results on stability and semi-classical limit in a semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping profile. The FQHD model can be used to analyze the thermal and quantum influences on the…
This article is dedicated to the investigation of the stabilization problem of a flexible beam attached to the center of a rotating disk. We assume that the feedback law contains a nonlinear torque control applied on the disk and nonlinear…
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_\infty$-output feedback controllers which stabilize the infinite dimensional system exponentially…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
This paper addresses the problem of feedback stabilization of a cascade of two heat equations that are coupled in the boundary conditions, the input being a boundary control for the first component of the cascade. Two distinct control input…
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 investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed.…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
The Casten-Holland and Matano theorem for interior reactions states that no nonconstant stable solutions exist in convex domains $\Omega$ of $\mathbb{R}^n$ under zero Neumann boundary conditions. In this paper we establish that the…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
In 1957, Mullins proposed surface diffusion motion as a model for thermal grooving. By adopting a small slope approximation, he reduced the model to the Mullins' linear surface diffusion equation, \begin{equation} \nonumber…
This paper studies the periodic feedback stabilization for a class of linear $T$-periodic evolution equations.Several equivalent conditions on the linear periodic feedback stabilization are obtained. These conditions are related with the…
Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally…
This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order that that of the nominal…