We investigate the problem of exact boundary controllability of semilinear onedimensional heat equations. We prove that it is possible to move from any steady-state to any other by means of a boundary control, provided that both are in the same connected component of the set of steady-states. The proof is based on an effective feedback stabilization procedure, which is implemented.

We investigate the nonhomogeneous initial boundary value problem for the Camassa-Holm equation on an interval. We provide a local in time existence theorem and a weak strong uniqueness result. Next we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law.

*Correspondence: [email protected] 2Department of Mathematics Education, Seowon University, Cheongju, 28674, South Korea Full list of author information is available at the end of the article Abstract In this paper, we are concerned with the general decay result of the quasi-linear wave equation for Kirchhoff type containing Balakrishnan-Taylor damping with a delay in the boundary feedback and a...

Experimental and theoretical studies of the excitability boundary for spiral wave behavior are presented. The boundary is defined by unstable wave segments, which are stabilized by using a negative-feedback control algorithm. A kinematic description of the constant-size, constant-shape wave segments is presented.

We study the local exponential stabilization of the 3D NavierStokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equation be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In orde...

In several experiments, observers tried to categorize stimuli constructed from two separable stimulus dimensions in the absence of any trial-by-trial feedback. In all of the experiments, the observers were told the number of categories (i.e., two), they were told that perfect accuracy was possible, and they were given extensive experience in the task (i.e., 800 trials). When the boundary separa...

This paper deals with the tracking control design for systems governed by linear parabolic partial differential equations with spatially and temporally varying coefficients and boundary input. For the boundary feedback control the backstepping method is applied, which allows to determine an exponentially stabilizing state feedback controller such that the closed-loop system behaves in the nomin...