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Displaying 81 –
100 of
133
This paper focuses on the analytical properties of the
solutions to the continuity equation with non local flow. Our
driving examples are a supply chain model and an equation for the
description of pedestrian flows. To this aim, we prove the well
posedness of weak entropy solutions in a class of equations
comprising these models. Then, under further regularity conditions,
we prove the differentiability of solutions with respect to the
initial datum and characterize this derivative. A necessary
...
We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...
We study an initial boundary-value problem for a wave
equation with time-dependent sound speed. In the control problem,
we wish to determine a sound-speed function which damps the
vibration of the system. We consider the case where the sound speed can
take on only two values, and propose a simple control law. We show
that if the number of modes in the vibration is finite, and none of
the eigenfrequencies are repeated, the proposed
control law does lead to energy decay. We illustrate the rich behavior
of...
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
We wish to show how the shock position in a nozzle could be
controlled. Optimal control theory and algorithm is applied to the
transonic equation. The difficulty is that the derivative with
respect to the shock position involves a Dirac mass. The one
dimensional case is solved, the two dimensional one is analyzed .
We study controllability for a nonhomogeneous string and ring under an axial stretching
tension that varies with time. We consider the boundary control for a string and
distributed control for a ring. For a string, we are looking for a control
f(t) ∈ L2(0,
T) that drives the state solution to rest. We show that for a ring, two forces
are required to achieve controllability. The controllability problem is reduced to a
moment problem...
We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model, microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time, related to the amount of analyticity of the...
We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the heat equation...
In this paper necessary and sufficient conditions of L∞-controllability and
approximate L∞-controllability are obtained for the control system
wtt = wxx − q2w,
w(0,t) = u(t),
x > 0, t ∈ (0,T), where
q ≥ 0, T > 0,
u ∈ L∞(0,T) is a control. This system is
considered in the Sobolev spaces.
In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
In this paper necessary and sufficient conditions of L∞-controllability and
approximate L∞-controllability are obtained for the control system
wtt = wxx − q2w,
w(0,t) = u(t),
x > 0, t ∈ (0,T), where
q ≥ 0, T > 0,
u ∈ L∞(0,T) is a control. This system is
considered in the Sobolev spaces.
In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...
In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...
In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
Currently displaying 81 –
100 of
133