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Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily...
This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the wave
equation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry of
the controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and an
energetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions...
This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, SIAM J. Control Optim. 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls...
We prove global internal controllability in large time for the nonlinear Schrödinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.
We discuss several global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed controls. First, based on the asymptotic analysis in vanishing time, we study the steering of the projections of its solution on any finite dimensional space spanned by the eigenfunctions for the truncated linear part. We show that, if the control-supporting area is properly chosen, then they can approximately...
In the first section of this paper we give a characterization of those closed convex cones (wedges) in the Lie algebra which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group , i.e., for which the subsemigroup generated by the exponential image of agrees with the whole group (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to compactly...
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