null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

well posedness of systems of linear elasticity with dirichlet boundary control and observation an open loop system of linear elasticity with dirichlet boundary control and collocated observation is considered the main result we obtained states that this system is well posed in the sense of salamon the result deduces the exponential stability of the closed loop system under proportional output feedback hence it answers positively an open question proposed by liu and krstic ima j appl math 65 2000 pp 109 121 moreover the well posedness together with the regularity of the open loop system in the sense of weiss that was obtained in our separate paper s g chai and b z guo feedthrough operator for linear elasticity system with boundary control and observation preprint school of computational and applied mathematics university of the witwatersrand south africa 2008 makes this infinite dimensional system parallel in many ways to a linear finite dimensional system in the framework of well posed and regular linear infinite dimensional systems

decay rates for the three dimensional linear system of thermoelasticity we consider the two and three dimensional system of linear thermoelasticity in a bounded smooth domain with dirichlet boundary conditions we analyze whether the energy of solutions decays exponentially uniformly to zero as t to infty first of all by a decoupling method we reduce the problem to an observability inequality for the lame system in linear elasticity and more precisely to whether the total energy of the solutions can be estimated in terms of the energy concentrated on its longitudinal component we show that when the domain is convex the decay rate is never uniform in fact the lack of uniform decay holds in a more general class of domains in which there exist rays of geometric optics of arbitrarily large length that are always reflected perpendicularly or almost tangentially on the boundary we also show that in three space dimensions the lack of uniform decay may also be due to a critical polarization of the energy on the transversal component of the displacement in two space dimensions we prove a sufficient and almost necessary condition for the uniform decay to hold in terms of the propagation of the transversal characteristic rays under the further assumption that the boundary of the domain does not have contacts of infinite order with its tangents we also give an example due to d hulin in which these geometric properties hold in three space dimensions we indicate without proof how a careful analysis of the polarization of singularities may lead to sharp sufficient conditions for the uniform decay to hold in two space dimensions we prove that smooth solutions decay polynomially in the energy space to a finite dimensional subspace of solutions except when the domain is a ball or an annulus finally we discuss some closely related controllability and spectral issues

canonical form of symplectic matrix pencils abstract we obtain a real canonical form for real symplectic pencils it extends earlier results which were derived over the complex field so that the canonical form was complex and which were limited to the case where the elementary divisors of eigenvalues on the unit circle have an even degree

sufficient excitation and stable reduced order adaptive iir filtering a perturbed error system is used to describe the parameter and output error behaviors of reduced order application of adaptive identifier filters such as the hyperstable adaptive recursive filter harf given satisfaction of a sufficient excitation condition this error system is shown to exhibit a bounded input bounded state bibs property this implies that despite order insufficiency the output and parameter estimates of harf and similar adaptive identifier filter algorithms remain bounded

on the existence of euler lagrange orbits satisfying the conormal boundary conditions abstract let m g be a closed connected riemannian manifold l t m r be a tonelli lagrangian given two non empty closed submanifolds q 0 q 1 m and a real number k we study the existence of euler lagrange orbits with energy k connecting q 0 to q 1 and satisfying suitable boundary conditions known as conormal boundary conditions we introduce the mane critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies we also provide counterexamples showing that all the results are sharp

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

normal forms of symplectic pencils and the discrete time algebraic riccati equation abstract the solution of the discrete time algebraic riccati equation leads to symplectic pencils of matrices normal forms of such pencils under symplectic equivalence are determined special attention is given to characteristic roots of modulus 1 and their corresponding elementary divisors and inertial invariants

stability of abstract thermo elastic semigroups abstract in this paper we characterize the stabilization for some thermo elastic type system with cattaneo law and we prove that the exponential or polynomial stability of this system implies a polynomial stability of the corresponding thermoelastic system with the fourier law the proof of the main results uses respectively the methodology introduced by haraux in 11 and generalized by ammari and tucsnak in 8 where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system and a characterization of the polynomial stability for a c 0 semigroup in a hilbert space by a polynomial estimation of the resolvent of its generator obtained by borichev and tomilov 9 illustrating examples are given

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

on the theory of thermoelasticity with microtemperatures abstract this paper studies the linear theory of thermoelastic materials with inner structure whose particles in addition to the classical displacement and temperature fields possess microtemperatures we discuss uniqueness results within the context of the dynamic boundary value problems under very mild assumptions upon the thermoelastic profile we also establish the relations describing the partition of the total energy in terms of the cesaro means of various types of component energies

a unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi discretized vibrating damped systems the liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations extensions to infinite dimensional settings have been studied by several authors see e g haraux 1991 11 and komornik and zuazua 1990 17 and references therein results on optimal energy decay rates under general conditions of the feedback is far from being complete the purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation we present a general approach based on convexity arguments to establish sharp optimal or quasi optimal upper energy decay rates for these systems and on comparison principles based on the dissipation property and interpolation inequalities in the infinite dimensional case for lower bounds of the energy we stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi discretized nonlinear damped vibrating pde s a part of this approach has been introduced in alabau boussouira 2004 2005 1 2 in the present paper we identify a new simple and explicit criteria to select a class of nonlinear feedbacks for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in alabau boussouira 2004 2005 1 2 moreover we prove optimality of the decay rates for this class in the finite dimensional case this class includes a wide range of feedbacks ranging from very weak nonlinear dissipation exponentially decaying in a neighborhood of zero to polynomial or polynomial logarithmic decaying feedbacks at the origin in the infinite dimensional case we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation this principle relies on suitable interpolation inequalities it allows us to give lower bounds for the energy of smooth initial data for the one dimensional wave equation with a distributed polynomial damping which improves haraux 1995 12 lower estimate of the energy for this case we also establish lower bounds in the multi dimensional case for sufficiently smooth solutions when such solutions exist we further mention applications of these various results to several classes of pde s namely the locally and boundary damped multi dimensional wave equation the locally damped plate equation and the globally damped coupled timoshenko beams system but it applies to several other examples furthermore we show that these optimal energy decay results apply to finite dimensional systems obtained from spatial discretization of infinite dimensional damped systems we illustrate these results on the one dimensional locally damped wave and plate equations discretized by finite differences and give the optimal energy decay rates for these two examples these optimal rates are not uniform with respect to the discretization parameter we also discuss and explain why optimality results have to be stated differently for feedbacks close to linear behavior at the origin

brief paper some properties of the output error method the output error identification method is studied in various respects the stationary points of the associated loss function are investigated sufficient conditions for a unique local minimum are given the loss functions can be minimized using a quasilinearization algorithm such an algorithm will give good local convergence it is however shown that global convergence does not always occur the output error method is also compared with some other estimation methods from the accuracy point of view it is proved that a prediction error method will give better accuracy an instrumental variable technique may give better or worse accuracy depending on the actual noise correlation

error surfaces of recursive adaptive filters for an adaptive filter with n adjustable coefficients or weights the error surface is a plot in n 1 dimensions of the mean squared error versus the n coefficient values if the adaptive filter is nonrecursive the error surface is a quadratic function of the coefficients with recursive adaptive filters the error surface is not quadratic and may even have local minima in this correspondence we discuss the nature of the recursive error surface and give examples of conditions under which local minima may exist we conclude with a discussion of the effects of the nonquadratic error surface on gradient search algorithms for recursive adaptive filters

indirect boundary stabilization of weakly coupled hyperbolic systems this work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations wherein only one of the equations is stabilized indirect damping see e g j math anal appl 173 1993 pp 339 358 we show that under a condition on the operators of each equation and on the boundary feedback operator the energy of smooth solutions of this system decays polynomially at infty we then apply this abstract result to several systems of partial differential equations wave wave systems kirchhoff petrowsky systems and wave petrowsky systems

on error surfaces of sufficient order adaptive iir filters proofs and counterexamples to a unimodality conjecture it is shown that although a conjecture proposed by s stearns ibid vol assp 29 p 763 6 june 1981 concerning sufficient conditions to guarantee unimodality of error surfaces for adaptive pole zero infinite impulse response iir filters is valid for first and second order filters it is not true in general without an additional constraint introduced by t soderstrom autom vol 11 p 93 9 jan 1982 proofs of the conjecture for a first and second order adaptive filters are given counterexamples are presented to illustrate the failure of this conjecture for higher order filters when the condition of soderstrom is not satisfied for both matching order and overparameterizing cases

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

blow up of solutions to the cauchy problem in nonlinear one dimensional thermoelasticity this paper is concerned with the blow up phenomena of solutions to the cauchy problem in non autonomous nonlinear one dimensional thermoelastic models obeying both fourier s law of heat flux and the theory due to gurtin and pipkin moreover some previously related results have been extended

quantum classical correspondence using projection operators classical properties associated with a large phase space domain with a smooth boundary as compared to the planck constant are shown to be expressed quantum mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis under the conditions of egorov s theorem the conservation of this correspondence under classical quantum dynamics is asserted

on transient error surfaces of output error iir adaptive filtering addresses the convergence of iir output error adaptive algorithms we argue that convergence to global or local optimum is simultaneously determined by the shape of the transient error surface and the convergence speed of the algorithm this argument is confirmed by simulation examples comparing the convergence of lms based and ls based algorithms

global carleman inequalities for parabolic systems and applications to controllability this paper has been conceived as an overview on the controllability properties of some relevant linear and nonlinear parabolic systems specifically we deal with the null controllability and the exact controllability to the trajectories we try to explain the role played by the observability inequalities in this context and the need of global carleman estimates we also recall the main ideas used to overcome the difficulties motivated by nonlinearities first we considered the classical heat equation with dirichlet conditions and distributed controls then we analyze recent extensions to other linear and semilinear parabolic systems and or boundary controls finally we review the controllability properties for the stokes and navier stokes equations that are known to date in this context we have paid special attention to obtaining the necessary carleman estimates some open questions are mentioned throughout the paper we hope that this unified presentation will be useful for those researchers interested in the field

existence of almost everywhere solution for nonlinear hyperbolic parabolic system in this paper the existence theorem for an almost everywhere solution of a mixed problem for more complicated nonlinear hyperbolic parabolic nonlinear thermoelasticity system was proved using galerkin s method and suitable a priori estimates were obtained

hermitian solutions of the equation x q nx 1n we consider the matrix equation x q nx 1n its hermitian solutions are parametrized in terms of the generalized lagrangian eigenspaces of a certain matrix pencil we show that the equation admits both a largest and a smallest solution the largest solution corresponds to the unique positive definite solution the smallest solution is the unique negative definite solution if and only if n is nonsingular if n is singular no negative definite solution exists an interesting relation between the given equation and a standard algebraic riccati equation of kalman filtering theory is also obtained finally we present an algorithm which converges to the positive definite solution for a wide range of initial conditions

optimal energy decay rate for partially damped systems by spectral compensation we study the stability of weakly coupled and partially damped systems by means of the riesz basis approach in higher dimensional spaces we propose a weaker structural damping that compensates for the behavior of the eigenvalues of the system therefore giving the optimal polynomial energy decay rate for smooth initial data

exponential stability of a mixture of two elastic solids with a degenerate weak damping mechanism abstract in this note we investigate stability issues for a mixture of two elastic solids the governing equations consist of two coupled systems of elastodynamic equations with a weak damping the damping involves the difference of velocities so that the damping operator is degenerate first we show that the underlying semigroup is strongly stable under a weaker parameters constraint thereby improving an earlier strong stability result of dafermos next we show that under extra appropriate constraints on the parameters of the coupled system the semigroup is exponentially stable our proof relies on the frequency domain method the multipliers technique and a seemingly new vector calculus identity lemma b our exponential stability result is new in the framework of mixtures involving elastodynamic equations with weak damping we also show that for some sets of parameters the system is asymptotically unstable in particular we use a concrete example to show that strong stability fails for a certain parameters constraint

a two level energy method for indirect boundary observability and controllability of weakly coupled hyperbolic systems this work is concerned with the boundary observability of an abstract system of two coupled second order evolution equations the coupling operator being a compact perturbation of the uncoupled system we assume that only one of the two components of the unknown is observed this is indirect observability we prove that by observing only one component one can get back a full weakened energy of both components under a compatibility condition linking the operators of each equation and for small coupling using the hilbert uniqueness method we then establish an indirect exact controllability result we apply this abstract result to several coupled systems of partial differential equations wave wave coupled elastodynamic systems petrowsky petrowsky and wave petrowsky systems

on the geometry of symplectic pencils arising from discrete time matrix equations abstract in this paper general symplectic matrix pencils are considered disregarding the particular matrix equations from which they arise a parameterization of the lagrangian deflating subspaces is given with the only assumption of regularity of the matrix pencil

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

periodic riccati difference equations approaching equilibria by implicit systems a parameterization of solutions to the periodic riccati difference equation rde is given by using behavioral tools the moving equilibria of the periodic rde are encompassed among the trajectories of the implicit ar model associated to the symplectic pencil of the corresponding hamiltonian equations this allows a parameterization of solutions of periodic rdes even in the case the dynamic matrix is singular

optimal decay rates and the selfadjoint property in overdamped systems abstract we deal with abstract linear strongly damped wave equations in the so called overdamped regime we show the occurrence of two interesting phenomena the first is the existence of an explicit special inner product which makes the problem selfadjoint the second is an improvement of the decay rate for more regular solutions that will be of an exponential polynomial type furthermore we prove the optimality of this decay rate

asymptotic expansion of the trace of the heat kernel associated to the dirichlet to neumann operator abstract for a given bounded domain with smooth boundary in a smooth riemannian manifold m g by decomposing the dirichlet to neumann operator into a sum of the square root of the laplacian and a pseudodifferential operator and by applying grubb s method of symbolic calculus for the corresponding pseudodifferential heat kernel operators we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to dirichlet to neumann operator as t 0 in particular we explicitly give the first four coefficients of this asymptotic expansion these coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the steklov problem

some new exact solutions for linear thermoelastic system the general analysis of transformation group method has been developed to study the linear thermoelastic system the application of one parameter group reduces the number of independent variables consequently the governing system of second order partial differential equations reduced into systems of ordinary differential equations in this paper some of these systems are solved analytically

time varying performance surfaces for adaptive iir filters geometric properties and implications for filter stability we present a new framework for understanding the performance of adaptive iir filters which enhances the understanding of filter stability during on line operation this new understanding arises from examining geometric properties of time varying performance surfaces which are defined by the data rather than the standard steady state error surfaces as defined by statistics of the data data dependent descent directions used in adaptive algorithms to update filter coefficients typically are viewed as functions of gradients defined on fixed performance surfaces and data is used to approximate these gradients at each iteration in contrast we view data dependent descent directions at each iteration as functions of exact gradients on time varying performance surfaces by examining the shape of these time varying performance surfaces near filter stability boundaries we are able to identify the origin of on line stability problems associated with existing adaptive iir filtering formulations and suggest corrective measures specifically by using exact z domain methods we define time varying performance surfaces which geometrically enforce filter stability and maintain the geometric and physical properties of the true error surface at each iteration development of adaptive algorithms based on this measure is expected to result in adaptive filters having improved stability performance during on line operation

some characteristics of error surfaces for insufficient order adaptive iir filters the error surfaces associated with insufficient order adaptive filters with white input are considered it is shown that some sufficient but not necessary conditions for multimodality of these surfaces can be identified a convenient method of determining the stationary points of some insufficient order adaptive filters with colored inputs is presented

geometry of the algebraic riccati equation part ii we prove that the set of real symmetric solutions of the algebraic riccati equation is isomorphic to the algebraic variety of invariant subspaces of a related n times n matrix by characterizing the structure of this variety we obtain a detailed description of the geometric properties of the solution set of the algebraic riccati equation

exponential decay of solutions in type ii porous thermo elasticity with quasi static microvoids abstract in this note we study the problem proposed by the one dimensional thermo porous elasticity of type ii with quasi static microvoids or in mathematical terms when the second time derivative of the volume fraction is so small that it can be negligible it is known that the isothermal deformations decay in a slow way here we prove that the introduction of a conservative mechanism as it is the type ii heat conduction makes the deformations damp generically in an exponential way which is a striking fact

gevrey regularity for a class of sums of squares of monomial vector fields abstract analytic or gevrey hypoellipticity is proved for a class of sums of squares of vector fields having a symplectic characteristic manifold of dimension 2 and arbitrary even codimension we note that this class contains examples for which the treves stratification seems to work as well as examples for which the treves stratification does not identify properly the non symplectic stratum

general matrix pencil techniques for the solution of algebraic riccati equations a unified approach we present a unified theory of matrix pencil techniques for solving both continuous and discrete time algebraic riccati equations ares under fairly general conditions on the coefficient matrices the theory applies to a large class of ares and riccati like equations arising from the singular h sup spl infin and h sup 2 control problems singular linear quadratic control the 4 block nehari problem or from singular j spectral factorizations the underlying concept is the so called proper deflating subspace of a possibly singular matrix pencil in terms of which necessary and sufficient conditions for the solvability of riccati equations are given it is shown that these conditions can be checked and the solutions computed by a numerically sound algorithm

complete determination of the singularity structure of zeta functions series of extended epstein type provide examples of non trivial zeta functions with important physical applications the regular part of their analytic continuation is seen to be a convergent or an asymptotic series their singularity structure is completely determined in terms of the wodzicki residue in its generalized form which is proven to yield the residua of all the poles of the zeta function and not just that of the rightmost pole obtainable from the dixmier trace the calculation is a very down to earth application of these powerful functional analytical methods in physics

on the propagation of polarization sets for systems of real principal type we define and study the polarization sets for vector valued distributions systems of real principal type are defined and we prove that for such systems of pseudodifferential operators we have a unique propagation of the polarization sets for the solutions

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

on the impossibility of localization in linear thermoelasticity in the middle of the 1990s green naghdi proposed three theories of thermoelasticity that they labelled as types i ii and ii the type ii theory which is also called thermoelasticity without energy dissipation is conservative and the solutions cannot decay with respect to time it is well known that in general in the linear theories of thermoelasticity of types i and iii the solutions decay with respect to time in many situations this decay is at least exponential in this paper we study whether this decay can be fast enough to guarantee the solutions to be zero in a finite time we investigate the impossibility of the localization in time of the solutions of linear thermoelasticity for the theories of green naghdi this means that the only solution that vanishes after a finite time is the null solution the main idea is to show the uniqueness of solutions for the backward in time problem to be precise for type iii thermoelasticity we will prove the impossibility of localization of solutions in the case of bounded domains and for the type i thermoelasticity in the case of exterior domains even when the solutions can be unbounded whether the spatial variable goes to infinity

controllability of two coupled wave equations on a compact manifold we consider the exact controllability problem on a compact manifold for two coupled wave equations with a control function acting on one of them only action on the second wave equation is obtained through a coupling term first when the two waves propagate with the same speed we introduce the time t omega rightarrow mathcal o rightarrow omega for which all geodesics traveling in go through the control region then through the coupling region mathcal o and finally come back in we prove that the system is controllable if and only if both and mathcal o satisfy the geometric control condition and the control time is larger than t omega rightarrow mathcal o rightarrow omega second we prove that the associated hum control operator is a pseudodifferential operator and we exhibit its principal symbol finally if the two waves propagate with different speeds we give sharp sufficient controllability conditions on the functional spaces the geometry of the sets and mathcal o and the minimal time