48 research outputs found
Boundary stabilization and control of wave equations by means of a general multiplier method
We describe a general multiplier method to obtain boundary stabilization of
the wave equation by means of a (linear or quasi-linear) Neumann feedback. This
also enables us to get Dirichlet boundary control of the wave equation. This
method leads to new geometrical cases concerning the "active" part of the
boundary where the feedback (or control) is applied. Due to mixed boundary
conditions, the Neumann feedback case generate singularities. Under a simple
geometrical condition concerning the orientation of the boundary, we obtain a
stabilization result in linear or quasi-linear cases
Energy decay for solutions of the wave equation with general memory boundary conditions
We consider the wave equation in a smooth domain subject to Dirichlet
boundary conditions on one part of the boundary and dissipative boundary
conditions of memory-delay type on the remainder part of the boundary, where a
general borelian measure is involved. Under quite weak assumptions on this
measure, using the multiplier method and a standard integral inequality we show
the exponential stability of the system.
Some examples of measures satisfying our hypotheses are given, recovering and
extending some of the results from the literature.Comment: 14 pages, submitted to Diff. Int. Eq
Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
In this paper, we shall prove a Carleman estimate for the so-called Zaremba
problem. Using some techniques of interpolation and spectral estimates, we
deduce a result of stabilization for the wave equation by means of a linear
Neumann feedback on the boundary. This extends previous results from the
literature: indeed, our logarithmic decay result is obtained while the part
where the feedback is applied contacts the boundary zone driven by an
homogeneous Dirichlet condition. We also derive a controllability result for
the heat equation with the Zaremba boundary condition.Comment: 37 pages, 3 figures. Final version to be published in Amer. J. Mat
On the cost of null-control of an artificial advection-diffusion problem
In this paper we study the null-controllability of an artificial
advection-diffusion system in dimension . Using a spectral method, we prove
that the control cost goes to zero exponentially when the viscosity vanishes
and the control time is large enough. On the other hand, we prove that the
control cost tends to infinity exponentially when the viscosity vanishes and
the control time is small enough.Comment: 16 page
On the local exact controllability of micropolar fluids with few controls
In this paper, we study the local exact controllability to special
trajectories of the micropolar fluid systems in dimension d = 2 and d = 3. We
show that controllability is possible acting only on one velocity.Comment: 25 pages, accepted for publication in ESAIM:COC
Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers.
17 pages, 9 figuresWe study the boundary stabilization of the wave equation by means of a linear or non-linear Neumann feedback. The rotated multiplier method leads to new geometrical cases concerning the active part of the boundary where the feedback is applied. Due to mixed boundary conditions, these cases generate singularities. Under a simple geometrical condition concerning the orientation of the boundary, we obtain stabilization results in both cases
Controllability and observabiliy of an artificial advection-diffusion problem
In this paper we study the controllability of an artificial
advection-diffusion system through the boundary. Suitable Carleman estimates
give us the observability on the adjoint system in the one dimensional case. We
also study some basic properties of our problem such as backward uniqueness and
we get an intuitive result on the control cost for vanishing viscosity.Comment: 20 pages, accepted for publication in MCSS. DOI:
10.1007/s00498-012-0076-
Result Certification of Static Program Analysers with Automated Theorem Provers
International audienceThe automation of the deductive approach to program veri- fication crucially depends on the ability to efficiently infer and discharge program invariants. In an ideal world, user-provided invariants would be strengthened by incorporating the result of static analysers as untrusted annotations and discharged by automated theorem provers. However, the results of object-oriented analyses are heavily quantified and cannot be discharged, within reasonable time limits, by state-of-the-art auto- mated theorem provers. In the present work, we investigate an original approach for verifying automatically and efficiently the result of certain classes of object-oriented static analyses using off-the-shelf automated theorem provers. We propose to generate verification conditions that are generic enough to capture, not a single, but a family of analyses which encompasses Java bytecode verification and FaÌhndrich and Leino type- system for checking null pointers. For those analyses, we show how to generate tractable verification conditions that are still quantified but fall in a decidable logic fragment that is reducible to the Effectively Propositional logic. Our experiments confirm that such verification conditions are efficiently discharged by off-the-shelf automated theorem provers
A Nelson-Oppen based Proof System using Theory Specific Proof Systems
International audienceSMT solvers are nowadays pervasive in verification tools. When the verification is about a critical system, the result of the SMT solver is also critical and cannot be trusted. The SMT-LIB 2.0 is a standard interface for SMT solvers but does not specify the output of the get-proof command. We present a proof system that is geared towards SMT solvers and follows their conceptually modular architecture. Our proof system makes a clear distinction between propositional and theory reasoning. Moreover, individual theories provide specific proof systems that are combined using the Nelson-Oppen proof scheme. We propose specific proof systems for linear real arithmetic (LRA) and uninterpreted functions (EUF) and discuss proof generation and proof checking. We have evaluated the cost of generating proofs in our proof system. Our experiments on benchmarks taken from the SMT-LIB library show that the simple mechanisms used in our approach suffice for a large majority of the selected benchmarks