The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We analyze the controllability of the wave equation on a cylinder when the control acts on the
boundary, that does not satisfy the classical geometric control condition.
We obtain precise estimates on the analyticity of reachable functions.
As the control time increases, the degree of analyticity that is required for a function to
be reachable decreases as an inverse power of time.
We conclude that any analytic function can be reached if that control time is large enough.
In the C∞ class, a...
We consider the one dimensional semilinear reaction-diffusion equation,
governed in Ω = (0,1) by controls, supported on any subinterval of
(0, 1), which are the functions of time only.
Using an asymptotic approach that we have previously introduced in [9],
we show that such a system is approximately controllable at any time in both
L2(0,1)( and C0[0,1], provided the nonlinear term f = f(x,t, u)
grows at infinity no faster than certain power of log |u|. The
latter depends on the regularity...
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
We consider a linear model of interaction between a viscous incompressible
fluid and a thin elastic structure located on a part of the fluid domain
boundary, the other part being rigid. After having given an existence and
uniqueness result for the direct problem, we study the question of
approximate controllability for this system when the control acts as a
normal force applied to the structure. The case of an analytic boundary has
been studied by Lions and Zuazua in [9]
where, in particular,...
We analyze the controllability of the motion of a fluid by means of the
action of a vibrating shell coupled at the boundary of the fluid. The
model considered is linear. We study its approximate controllability,
i.e. whether the fluid may reach a dense set of final configurations at
a given time. We show that this problem can be reduced to a unique
continuation question for the Stokes system. We prove that this unique
continuation property holds generically among analytic domains and
therefore,...
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly...
Currently displaying 41 –
60 of
62