a stability result for linear parameter varying systems abstract a negative real part eigenvalue assumption on a linear parameter varying system implies exponential stability under a condition that includes either slowly varying parameters or slowly accelerating parameters

renormalised solutions of nonlinear parabolic problems with l1 data existence and uniqueness in this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem where the data f and u 0 belong to l 1 0 t and l 1 and where the function a 0 t n n is monotone but not necessarily strictly monotone and defines a bounded coercive continuous operator from the space into its dual space the renormalised solution is an element of c 0 0 t l 1 such that its truncates t k u belong to with this solution satisfies the equation formally obtained by using in the equation the test function s u where belongs to and where s belongs to c with

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

quadratic stability and stabilization of linear systems with frobenius norm bounded uncertainties in this paper a quadratic stability condition and a quadratic stabilizer are proposed for linear systems with frobenius norm bounded uncertainties the necessary and sufficient condition for the quadratic stability of the uncertain system is given by a riccati inequality the proposed state feedback quadratic stabilizer can be obtained by solving a riccati equation

nonlinear parabolic equations with measure data in this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model isu div u p 2 u on 0 t p with homogeneous cauchy dirichlet boundary conditions wherep 1 and is a bounded measure on 0 t we also study how the summability of the gradient improves if the measure is a function inlm 0 t withm small moreover we give a new proof of the existence of a solution for problem p

stability for the multifrequency inverse medium problem abstract the solution of a multi frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies in this paper rigorous stability estimates are derived when the frequency takes value in a bounded interval it is showed that the ill posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger more precisely under certain regularity assumptions on the refractive index the estimates indicate that the power in holder stability is an increasing function of the largest value in the frequency band finally a lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula

necessary and sufficient conditions for quadratic stability and stabilizability of uncertain linear time varying systems in this paper we consider linear time varying systems subject to norm bounded one block structured uncertainties first given an unforced system we find necessary and sufficient conditions for quadratic stability then considered a controlled system we provide necessary and sufficient conditions for quadratic stabilizability both for the state and the output feedback case

hyperbolic geometry and local dirichlet neumann map abstract we show in three dimensions that if we know the dirichlet to neumann dn map associated to the schrodinger equation with a potential around the intersection of a sphere centered outside the convex hull of a bounded domain with smooth boundary we can determine uniquely the corresponding spherical mean of the potential with an appropriate measure this allows one to determine the potential near the boundary where the dn map is measured similar results are valid for electrical impedance tomography

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

stability estimates for the calderon problem with partial data this is a follow up of a previous article where we proved local stability estimates for a potential in a schr odinger equation on an open bounded set in dimension n 3 from the dirichlet to neumann map with partial data the region under control was the penumbra delimited by a source of light outside of the convex hull of the open set these local estimates provided stability of log log type corresponding to the uniqueness results in calder on s inverse problem with partial data proved by kenig sj ostrand and uhlmann in this article we prove the corresponding global estimates in all dimensions higher than three the estimates are based on the construction of solutions of the schr odinger equation by complex geometrical optics developed in the anisotropic setting by dos santos ferreira kenig salo and uhlmann to solve the calder on problem in certain admissible geometries

strong regularizing effect of a gradient term in the heat equation with the hardy potential abstract we deal with the following parabolic problem u t u u p u x 2 f u 0 in 0 t u x t 0 on 0 t u x 0 u 0 x x where r n n 3 is a bounded regular domain such that 0 or r n 1 p 2 0 and f 0 u 0 0 are in a suitable class of functions for p p n n 1 we will show that the above problem has a solution for all 0 f l 1 t and u 0 l 1 we prove also that p is optimal for the existence result these results prove the strong regularizing effect of a gradient term in the problem studied in baras and goldstein 1984 3 the cauchy problem is also studied

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

a review of some recent results on the output least squares formulation of parameter estimation problems abstract in this paper recent advances in the analysis of the output least squares formulation of parameter estimation problems for distributed parameter systems are summarized we address problems of identifiability discuss the notion of output least squares stability involving tikhonov regularization in a nonlinear environment give results on the approximation of these infinite dimensional problems by finite dimensional ones and review numerical techniques

on the uniqueness of inverse problems from incomplete boundary data we present a generalization of our previous results on the uniqueness of inverse coefficient problems for elliptic equations the theorem proved here is formulated for piecewise constant coefficients with piecewise smooth interfaces of discontinuities which require local boundary data we consider problems with coefficients unknown at one side as well as at both sides of the boundary the uniqueness of the former is proven the latter can yield up to two solutions the proofs are based on a simple analysis of singularities of the green functions the presented approach exactly conforms to some important inverse problems arising in applications of electromagnetic geophysics

identifiablity under approximation for an elliptic boundary value problem necessary and sufficient conditions for identifiability of the diffusion coefficient in galerkin approximations to a two point boundary value problem are derived for various choices of galerkin subspaces the results are further used to investigate output least squares identifiability and output least squares stability of the diffusion coefficient

a real time algorithm for the location search of discontinuous conductivities with one measurement we consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current voltage observation we develop a real time algorithm for determining the location of the anomaly this new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage combined with the size estimation result this algorithm gives a good initial guess for newton type schemes we give the rigorous proof for the location search algorithm both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast stable and efficient 2001 john wiley sons inc

probing for electrical inclusions with complex spherical waves let a physical body in 2 or 3 be given assume that the electric conductivity distribution inside consists of conductive inclusions in a known smooth background further assume that a subset is available for boundary measurements it is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on more precisely given a ball b with center outside the convex hull of and satisfying b boundary measurements on with explicitly given dirichlet data are enough to determine whether b intersects the inclusion an approximate detection algorithm is introduced based on the theory numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion free domain near and is robust against measurement noise 2007 wiley periodicals inc

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

inherent identifiability of parameters in elliptic differential equations together with appropriate boundary conditions for u on the boundary r of q for given a and f this is a well known equation in the unknown u we shall consider the inverse problem which givenf consists in determining a from u more precisely we study the question of uniqueness and continuous dependence of a in terms of u the uniqueness problem is generally referred to as the identifiability problem well known contributions are the borg and the gelfand levitan theories which require knowledge of spectral data of 1 1 see 5 61 for recent work an identifiability of a from neumann boundary data for all g in the elliptic equation v avu o 1 f g we refer to s the problem of continuous dependence of a with respect to u is of equal importance as identifiability but has received much less attention so far in 121 the study of the inverse problem associated with 1 1 is based on the observation that 1 1 is a hyperbolic equation in a employing the method of characteristics a continuous dependence analysis is given under combinations of the assumptions vul 0 and ldul 0 in this paper we concentrate on uniqueness and continuous dependence results without a priori assumptions on the sign of vul the basic and very simple idea for which we give an analytical justification is that a in 1 1

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

uniqueness for formally determined inverse boundary value problems abstract in this paper we study the inverse conductivity problem in two dimensions this problem is reduced to a formally determined inverse boundary value problem for the schrodinger equation some recent generic uniqueness results for the inverse problems will be discussed and a new continuous dependence result presented

on the construction of a potential from cauchy data abstract we investigate the problem of recovering a potential q y in the differential equation u q y u 0 x y 0 1 0 1 u 0 y u 1 y u x 0 0 u x 1 f x u y x 1 g x the method of separation of variables reduces the recovery of q y to a nonstandard inverse sturm liouville problem an asymptotic formula is developed that suggests that under appropriate conditions on the cauchy pair f g q y is uniquely determined up to the mean moreover the recovery of q y is comparable to finding a function from its polynomial moments a reconstruction scheme is suggested and numerical examples are considered

an approach for computing the exact stability domain for a class of lti parameter dependent systems in this paper the complete stability domain for both single and multi parameter dependent lti systems is synthesized by extending existing results in the literature this domain is calculated through a guardian map which involves the determinant of the kronecker sum of a matrix with itself the single parameter case is easily computable whereas the multi parameter case is more involved the determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity of the results presented in this paper

a multiscale theory for image registration and nonlinear inverse problems abstract in an influential paper tadmor et al 2004 42 introduced a hierarchical decomposition of an image as a sum of constituents of different scales here we construct analogous hierarchical expansions for diffeomorphisms in the context of image registration with the sum replaced by composition of maps we treat this as a special case of a general framework for multiscale decompositions applicable to a wide range of imaging and nonlinear inverse problems as a paradigmatic example of the latter we consider the calderon inverse conductivity problem we prove that we can simultaneously perform a numerical reconstruction and a multiscale decomposition of the unknown conductivity driven by the inverse problem itself we provide novel convergence proofs which work in the general abstract settings yet are sharp enough to prove that the hierarchical decomposition of tadmor nezzar and vese converges for arbitrary functions in l 2 a problem left open in their paper we also give counterexamples that show the optimality of our general results

inverse problems for metal oxide semiconductor field effect transistor contact resistivity inverse problems arising from the identification of transistor contact resistivity and contact window location are studied a one point boundary measurement of the potential is shown to be sufficient to identify each from a one parameter monotone family and such identification is both stable and continuously dependent on the parameter for a nonmonotone family of locations with resistivity given similar results are obtained for measurement made on almost all boundary points

guardian map approach to robust stability of linear systems with constant real parameter uncertainty new sufficient conditions are derived for stability robustness of linear time invariant state space systems with constant real parameter uncertainty these bounds are obtained by applying a guardian map to the uncertain system matrices since this approach is only valid for constant real parameter uncertainty these bounds do not imply quadratic stability which guarantees robust stability with respect to time varying uncertainty but is often conservative with respect to constant real parameter uncertainty numerical results are given to compare the new bounds with bounds obtained previously by means of lyapunov methods

the heat equation with a singular potential of concern is the singular problem du dt au c x 2 iz x tz x 0 u0 x and its generalizations here c 0 x g rn t 0 and and t 0 are nonnegative and not both identically zero there is a dimension dependent constant c n such that the problem has no solution for c ct n for c s ct a necessary and sufficient conditions are found for and u0 so that a nonnegative solution exists

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

inverse boundary value problems at the boundary continuous dependence we use the methods of microlocal analysis to give a new proof of a theorem of kohn and vogelius showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary moreover we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

identification problems in linear elasticity let be a bounded domain inrnwithc2 boundary and letdbe a lipschitz domain withd we consider the inverse problem determiningd to the system of linear elasticitydi d ij rs ir js d ir js djus 0in where d d rn dand d d rn d under the condition on the lame constants 0 we show thatdis uniquely determined by the complete knowledge of the dirichlet to neumann map we also obtain an uniqueness result for the monotone case from one boundary measurement

a c0 finite element method for an inverse problem a c 0 finite element method is presented for an inverse problem in which the coefficient in the differential operator is to be determined from the measurement of the solution of a boundary value problem the unknown in the inverse problem is approximated by a minimizer of a cost function that includes both the output error and equation error error estimates in a weighted h 1 norm and l 2 are given numerical examples are presented to show features of the method

electrical impedance tomography by elastic deformation this paper presents a new algorithm for conductivity imaging our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations using asymptotics of the fields in the presence of small volume inclusions we relate the pointwise values of the energy density to the measured data through a nonlinear pde our algorithm is based on this pde and takes full advantage of the enriched data we give numerical examples that illustrate the performance and the accuracy of our approach

the cauchy problem for ut δu u q with q a positive real number the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces in that context it is known as the generalized deterministic kpz equation the paper is concerned with the initial value problem for the equation under the assumption that the initial data function is bounded and continuous results on the existence uniqueness and regularity of solutions are obtained

on the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term we study questions of existence uniqueness and asymptotic behaviour for the solutions of u x t of the problem begin gathered text u t delta u lambda e u text lambda text 0 t 0 text x text varepsilon b hfill p text u x 0 u 0 x text x text varepsilon b hfill text u x t 0 text on text partial b times 0 infty hfill end gathered where b is the unit ball x varepsilon r n x text leqq text 1 text and n geqq 3 our interest is focused on the parameter 0 2 n 2 for which p admits a singular stationary solution of the form s x 2log x

an inverse polynomial method for the identification of the leading coefficient in the sturm liouville operator from boundary measurements an inverse polynomial method of determining the unknown leading coefficient k k x of the linear sturm liouville operator au k x u x q x u x x 0 1 is presented as an additional condition only two measured data at the boundary x 0 x 1 are used in absence of a singular point u x 0 u x 0 x 0 1 the inverse problem is classified as a well conditioned if there exists at least one singular point then the inverse problem is classified as moderately ill conditioned u x 0 0 x 0 0 1 u x 0 x x 0 u x 0 x 0 1 and severely ill conditioned u x 0 u x 0 0 x 0 0 1 u x 0 u x 0 x x 0 for each of the cases direct problem solution is approximated by corresponding polynomials and the inverse problem is reformulated as a cauchy problem for to the first order differential equation with respect the unknown function k k x an approximate analytical solution of the each cauchy problems are derived in explicit form numerical simulations all the above cases are given for noise free and noisy data an accuracy of the presented approach is demonstrated on numerical test solutions

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

parameter dependent lyapunov functions and the popov criterion in robust analysis and synthesis many practical applications of robust feedback control involve constant real parameter uncertainty whereas small gain or norm bounding techniques guarantee robust stability against complex frequency dependent uncertainty thus entailing undue conservatism since conventional lyapunov bounding techniques guarantee stability with respect to time varying perturbations they possess a similar drawback in this paper we develop a framework for parameter dependent lyapunov functions a less conservative refinement of fixed lyapunov functions an immediate application of this framework is a reinterpretation of the classical popov criterion as a parameter dependent lyapunov function this result is then used for robust controller synthesis with full order and reduced order controllers

optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a hardy potential abstract we deal with the following parabolic problem u t u u p u x 2 f u 0 in 0 t u x t 0 on 0 t u x 0 u 0 x x where r n n 3 is a bounded regular domain such that 0 or r n p 1 0 and f 0 u 0 0 are in a suitable class of functions there are deep differences with respect to the heat equation 0 the main features in the paper are the following if 0 there exists a critical exponent p such that for p p there is no nontrivial local solution p is optimal in the sense that if p p there exists solution for suitable data if we consider the cauchy problem i e r n we find the same phenomenon about the critical power p as above moreover there exists a fujita type exponent f p in the sense that independently of the initial datum for 1 p f any solution blows up in a finite time respect to an integral norm this is a major difference with respect to the heat equation 0

improving and estimating the accuracy of strassen s algorithm fast matrix multiplication algorithms of strassen and winograd are known to have weaker numerical accuracy than usual inner product multiplication in this paper we show that scaling usually improves accuracy when operands have elements of widely varying magnitude we also propose estimators for numerical errors based on samples of the result all these estimators can be computed in o n 2 operations experiments prove the effectiveness of the scaling idea and of the absolute error estimator

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

singular solutions of elliptic equations and the determination of conductivity by boundary measurements abstract we improve some results on uniqueness and stability in the determination of the coefficient a in the equation i div a grad u 0 in when all possible pairs of dirichlet and neumann data on are known we also treat cases of anisotropic equations our method relies on the construction of solutions to i having an isolated singularity with prescribed asymptotic behaviour

an inverse problem for the steady state diffusion equation we consider the problem of identifying a spatially varying diffusion coefficient using an observed solution to the forward problem under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient we develop some continuous dependence results for this problem and also propose a particularly advantageous set of test conditions for observing the forward solution

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

electrical conductivity reconstruction using nonlocal boundary conditions in this paper we study existence uniqueness and solution estimates to the mixed problem nabla cdot sigma nabla u 0 with dirichlet to neumann map boundary conditions and neumann boundary conditions we then show how this can be used in the reconstruction of sigma given the relationship between u and its normal derivative on the boundary portion where we do not apply the dirichlet to neumann map a numerical reconstruction scheme is also derived

on the continuum limit of a discrete inverse spectral problem on optimal finite difference grids we consider finite difference approximations of solutions of inverse stur m liouville problems in bounded intervals using three point finite difference sc hemes we discretize the equations on so called optimal grids constructed as follow s for a staggered grid with 2k points we ask that the finite difference operator a k k jacobi matrix and the sturm liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval this requirement determines uniquely the entries in the jacobi matrix which are grid cell averages of the coefficients in the continuum problem if these coefficients are known we can find the grid which we call optimal becau se it gives by design a finite difference operator with a prescribed spectr al measure we focus attention on the inverse problem where neither the coefficients n or the grid are known a key question in inversion is how to parametrize the coefficients i e how to choose the grid it is clear that to be successful this grid must be close to the optimal one which is unknown fortunately as we show here the grid dependence on the unknown coefficients is weak so the inversion can be done on a pr ecomputed grid for an a priori guess of the unknown coefficients this obse rvation leads to a simple yet efficient inversion algorithm which gives coefficien ts that converge pointwise to the true solution as the number k of data points tends to infinity the cornerstone of our convergence proof is showing that op timal grids provide an implicit natural regularization of the inverse problem by givin g reconstructions with uniformly bounded total variation the analysis is based on a novel explicit perturbation analysis of lanczos recursions and on a discrete

robust performance analysis with lmi based methods for real parametric uncertainty via parameter dependent lyapunov functions robust performance analysis for linear time invariant systems with linear fractional transformation real parametric uncertainty is considered new conditions of robust stability performance based on parameter dependent lyapunov functions are proposed the robust stability performance measures are robust pole location robust h sub spl infin performance and robust h sub 2 performance linear matrix inequality lmi based sufficient conditions for the existence of parameter dependent lyapunov functions are derived by using the quadratic separation concept the performances of the proposed conditions are compared with existing tests