Related papers: Controllability of a linear system with persistent…
In this paper we consider a viscoelastic three dimensional body (of Maxwell-Boltzmann type) controlled on (part of) the boundary. We assume that the material is isotropic and homogeneous. If the body is elastic (i.e. no dissipation due to…
In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary…
In this paper we study controllability of a linear equation with persistent memory when the control belongs to $ H^k_0(0,T;L^2(\ZOMq)) $. In the case the memory is zero, our equation is reduced to the wave equation and a result due to…
We are motivated by the problem of control for a non-homogeneous elastic string with memory. We reduce the problem of controllability to a non-standard moment problem. The solution of the latter problem is based on an auxiliary Riesz basis…
It is now well understood that equations of viscoelasticity can be seen as perturbation of wave type equations. This observation can be exploited in several different ways and it turns out that it is a usefull tool when studying…
Treatises on vibrations devote large space to study the dynamical behavior of an elastic system subject to known external tractions. In fact, usually a "system" is not an isolated body but it is part of a chain of mechanisms which disturb…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…
The semilinear beam equation with impulses, memory and delay is considered. We obtain the approximate controllability. This is done by employing a technique that avoids fixed point theorems and pulling back the control solution to a fixed…
In this paper we solve the problem of the identification of a coefficient which appears in the model of a distributed system with persistent memory encountered in linear viscoelasticity (and in diffusion processes with memory). The…
We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial…
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…
We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods.…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear viscoelasticity. We begin by examining the physical foundations of Boltzmann and…
Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. The paper concerns about the exact…
The following fact is known for large classes of distributed control systems: when the target is regular, there exists a regular steering control. This fact is important to prove convergence estimates of numerical algorithms for the…