global attractor for the kirchhoff type equation with a strong dissipation abstract the paper studies the longtime behavior of the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the related continuous semigroup s t possesses in the phase space with low regularity a global attractor which is connected and an example is shown

weakly damped quasilinear wave equation existence of time periodic solutions among many questions concerning global behaviour of hyperbolic equations the existence of time periodic solutions seems to be of great interest both from the mathematical and physical points of view the aim of the present paper is to add to the vast literature on that subject a result related to the weakly damped quasilinear wave equation see section 1 theorem 1 with a function u u x t of x e 0 1 t e r consider the equation

a novel wavelet based generalized sidelobe canceller this paper presents a novel narrow band adaptive beamformer with the generalized sidelobe canceller gsc as the underlying structure the new beamformer employs a wavelet based approach for the design of the blocking matrix of the gsc which is now constituted by a set of regular m band wavelet filters such a construction of the blocking matrix can not only block the desired signals from the lower path as required provided the wavelet filters have sufficiently high regularity but it also encompasses the widely used one with ones and minus ones along the diagonals as a special case in addition it possesses two advantageous features first the eigenvalue spreads of the covariance matrices of the blocking matrix outputs as demonstrated in various scenarios are decreased as compared with those of previous approaches since the popular least mean squares lms algorithm has been notorious for its slow convergence rate the reduction of the eigenvalue spreads can in general accelerate the convergence speed of the succeeding lms algorithm second the new beamformer belongs to a specific type of partially adaptive beamformers wherein only a portion of the available degree of freedom is utilized in the adaptive processing as such the overall computational complexity is substantially reduced when compared to previous works the issues of choosing the parameters involved for superior performance are also addressed simulation results are furnished as well to justify this new approach

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

a robust adaptive generalized sidelobe canceller with decision feedback conventional generalized sidelobe canceller gsc is sensitive to a mismatch between the estimated and actual direction of arrival doa of the desired signal such a mismatch induces signal cancellation in the gsc and it severely degrades the beamforming performance in this paper we propose a new decision feedback df technique to increase the robustness against the doa mismatch our new scheme introduces a blind equalizer and a feedback filter in the gsc structure we first derive wiener solutions for the df gsc with perfectly matched and mismatched doa and show that the problem of signal cancellation can be avoided then we consider the adaptive gsc implementation in which the least mean square lms algorithm is used for weight adaptation in addition to the improved robustness the proposed scheme also remedies the slow convergence problem inherent in the conventional adaptive gsc structure the convergence behavior of the lms based df gsc is fully analyzed and the analytic signal to interference plus noise ratio sinr is also derived finally simulation results demonstrate that while the proposed structure can considerably enhance the overall performance it has greatly improved robustness as compared to other existing robust adaptive beamformers

optimal antenna currents for q superdirectivity and radiation patterns using convex optimization the high q factor low bandwidth and low efficiency make the design of small antennas challenging here convex optimization is used to determine current distributions that provide upper bounds on the antenna performance optimization formulations for maximal gain q factor quotient minimal q factor for superdirectivity and minimum q for given far fields are presented the effects of antennas embedded in structures are also discussed the results are illustrated for planar geometries

field patterns of resonant noncircular closed loop arrays further analysis previous papers have introduced the continuous current model for resonant closed loop arrays of cylindrical dipoles and for a certain class of array shapes have determined the resulting field patterns analytically those analytical calculations involve several approximations in the present paper we first study the aforementioned model numerically for the case of elliptical closed loop arrays the results which involve fewer approximations than those of the previous papers but which refer to different array shapes imply that elliptical arrays have a bidirectional highly directive field and unlike conventional arrays have no sidelobes combining analytical and numerical methods we then investigate the relationship between the aforementioned continuous current model and what we call the discrete current model which in a certain sense is more realistic the results indicate that subject to suitable conditions the two models yield virtually identical results in our analytical investigations an important tool is the poisson summation formula for finite sums we have devoted a stand alone section to this formula which supplements recent unrelated publications in antenna theory

a new set of linear constraints for broad band time domain element space processors a new set of linear constraints for designing broad band time domain element space antenna array processors is presented the set of linear constraints is used to ensure that a desired look direction response of the processor over a frequency band of interest can be closely approximated the design technique is posed in such a way that three types of presteering can be handled no presteering coarse presteering and exact presteering the elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors the relationship that the new processor has to other broad band processors is also established furthermore the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation

performance analysis of derivative constraint adaptive arrays with pointing errors the performance of adaptive arrays with arbitrary order derivative constraints to avoid the signal nulling caused by the error in the steering angle is investigated the generalized sidelobe canceller gsc is used to evaluate the bearing responses of adaptive arrays with pointing errors under the assumption of equispaced linear arrays the legendre polynomial is used to derive a closed form formula for the sidelobe leakage factor the ratio in which the signal leaks into the gsc sidelobe cancelling branch moreover the effective beamwidth the maximum range of pointing inaccuracy allowable to keep the signal loss in array output less than a given value is derived for the gsc with a delay and sum quiescent beamformer such adaptive arrays can achieve the maximum output signal to noise ratio when the presteering is perfect and the performance is independent of the location of the phase origin numerical results are presented to confirm the analysis

asymptotic behavior of solutions to the damped quasilinear equation 2 t2 u x t γ u t x t xσ u x x t 0 abstract asymptotic lower bounds for the l 2 norms of solutions of initial boundary value problems associated with the equation of the title are derived for a simple case in which the equation fails to exhibit strict hyperbolicity it is shown that in such cases it can be expected that the norm of a solution will be bounded away from zero as t even as the damping factor becomes infinitely large

surface wave and superdirectivity aspects of effective current for linear antennas previous papers have defined the concept of effective current for linear antennas as a method of postprocessing the unphysical solutions obtained by applying discretization galerkin methods to the usual integral equations that employ the approximate or reduced kernel such an unphysical solution can be thought of as an auxiliary rapidly oscillating current located on the axis of the linear antenna while the effective current is the magnetic field due to the oscillating current at a distance equal to the antenna radius multiplied by a factor equal to the antenna circumference in the present paper we focus on the rapid decrease of the aforementioned magnetic field and point out similarities to surface waves to the well known phenomenon of superdirectivity and to the method of auxiliary sources mas our study sheds light on the unusual nature of electromagnetic waves generated by currents with very rapid spatial variations subject to the condition that the discretization is fine we treat th

the use of the frill generator in thin wire integral equations for a frill generator feed certain fundamental mathematical properties of hallen s and pocklington s equations with the approximate kernel are stated and derived for a particular moment method procedure galerkin s method with pulse functions applied to hallen s equation the consequences to the numerical solutions are carefully examined generalizations to other numerical methods with subsectional basis functions are discussed many of our results come from studying the simpler problem of the infinite dipole analytically and applying the understanding thus obtained to the case of the finite dipole

performance analysis of a wavelet based generalized sidelobe canceller in this paper we carry out a detailed performance analysis of the recently addressed wavelet based generalized sidelobe canceller gsc which employs a set of p regular m band wavelet filters in the design of the blocking matrix involved we begin our analysis by developing a closed form expression of the output signal to interference plus noise ratio sinr of partially adaptive beamformers with the gsc as the underlying structure under a one jammer or multiple jammer environment this new expression is shown to encompass several previous works as special cases we then examine the relationship between the choices of the parameters p and m in the wavelet based gsc and the corresponding output sinr based on this expression some guidelines for the choices of these parameters can thus be induced to achieve superior performance simulation results are also furnished to justify these suggestions

global existence for quasi linear dissipative wave equations with large data and small parameter on considere le probleme aux valeurs initiales pour les equations d onde quasi lineaires eu t u x 0 t u x 0 u x 0 u 0 x x 0 0 x ou e 0 0 t r x r u et sont des fonctions scalaires de x t et est une fonction donnee croissante lisse sur r on etudie le comportement des solutions classiques pour t grand

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

optimal currents on arbitrarily shaped surfaces an optimization problem has been formulated to find a resonant current extremizing various antenna parameters the method is presented on but not limited to particular cases of gain g quality factor q gain to quality factor ratio g q and radiation efficiency eta of canonical shapes with conduction losses explicitly included the rao wilton glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated by switching to another basis generated by a specific eigenvalue problem it is finally shown that the optimal current can in principle be found as a combination of a few eigenmodes the presented method constitutes a general framework in which the antenna parameters expressed as bilinear forms can automatically be extremized

on methods to determine bounds on the q factor for a given directivity this paper revisit and extend the interesting case of bounds on the q factor for a given directivity for a small antenna of arbitrary shape a higher directivity in a small antenna is closely connected with a narrow impedance bandwidth the relation between bandwidth and a desired directivity is still not fully understood not even for small antennas initial investigations in this direction have related the radius of a circumscribing sphere to the directivity and bounds on the q factor have also been derived for a partial directivity in a given direction in this paper we derive lower bounds on the q factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semidefinite relaxation sdr techniques we also show that the relaxed solution is also a solution of the original problem of determining the lower q factor bound for a total desired directivity sdr can also be used to relax a class of other interesting nonconvex constraints in antenna optimization such as tuning losses and front to back ratio we compare two different new methods to determine the lowest q factor for arbitrary shaped antennas for a given total directivity we also compare our results with full electromagnetic simulations of a parasitic element antenna with high directivity

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

system identification using nonstationary signals the conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output it is equivalent to identifying the frequency response of the system by calculating the empirical cross spectrum between the system s input and output divided by the empirical auto spectrum of the input process however if the additive noise at the system s output is correlated with the input process e g in case of environmental noise that affects both system s input and output the method may suffer from a severe bias effect we present a modification of the cross spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise the proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation when the desired signal is nonstationary in nature e g speech or image

long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term iii on considere des solutions lisses du probleme aux valeurs initiales hyperbolique quasilineaire eu tt u t ij 1 n a ij i j u 0 u 0 u 0 u t 0 u 1 ou e 0 0 u u x t r x r n on etudie l existence de solutions globales correspondant a des donnees arbitrairement grandes initiales u 0 et u 1 et a leur convergence quand e 0 vers la solution du probleme parabolique correspondant

analysis of the power spectral deviation of the general transfer function gsc in recent work we considered a microphone array located in a reverberated room where general transfer functions tfs relate the source signal and the microphones for enhancing a speech signal contaminated by interference it was shown that it is sufficient to use the ratio between the different tfs rather than the tfs themselves in order to implement the suggested algorithm an unbiased estimate of the tfs ratios was obtained by exploiting the nonstationarity of the speech signal in this correspondence we present an analysis of a distortion indicator namely power spectral density psd deviation imposed on the desired signal by our newly suggested transfer function generalized sidelobe canceller tf gsc algorithm it is well known that for speech signals psd deviation between the reconstructed signal and the original one is the main contribution for speech quality degradation as we are mainly dealing with speech signals we analyze the psd deviation rather than the regular waveform distortion the resulting expression depends on the tfs involved the noise field and the quality of estimation of the tf s ratios for the latter dependency we provide an approximated analysis of estimation procedure that is based on the signal s nanstationarity and explore its dependency on the actual speech signal and on the signal to noise ratio snr level the theoretical expression is then used to establish empirical evaluation of the psd deviation for several tfs of interest various noise fields and a wide range of snr levels it is shown that only a minor amount of psd deviation is imposed on the beamformer output the analysis presented in this correspondence is in good agreement with the actual performance presented in the former tf gsc paper

existence of global smooth solutions to the initial boundary value problem for the quasi linear wave equation with a degenerate dissipative term let c be a bounded domain with smooth boundary dq in the n dimen sional euclidean space rn and let us consider the initial boundary value problem for the classical quasi linear wave equation with a dissipation u v a lvul vu u x u o in qx o ce 4x 0 uo

performance limits of the broadband generalized sidelobe cancelling structure in an isotropic noise field in acoustic applications the signal source of interest is generally broadband and the background noise field is predominantly isotropic in this letter the performance of the broadband generalized sidelobe canceller optimized with respect to an isotropic noise field is analyzed and compared against the performance of the conventional summing beamformer the comparison is based on an ideal continuous time infinite length generalized sidelobe canceller with the aim of determining the performance limits of this beamforming structure

a spatial filtering approach to robust adaptive beaming the problem of controlling the superresolution in adaptive beamformers is treated a straightforward method is presented that works for both narrowband and broadband arrays the method is based on forming the blocking matrix in a general sidelobe canceller structure using a spatial fir filter the suppression of this spatial filter and the implicit noise of the leaky least mean square algorithm together determine the beamformer

global existence of classical solutions to the initial boundary value problem of the semilinear wave equations with a degenerate dissipative term we consider the initial boundary value problem for a typical semilinear wave equation u tt u u 2k 1 0 on 0 u x 0 u 0 x u t x 0 u 1 x and u x t 0 where k is a positive integer

original and modified kernels in method of moments analyses of resonant circular arrays of cylindrical dipoles properly dimensioned circular arrays of cylindrical dipoles are known to possess very narrow resonances it is also known that analyzing such arrays using moment methods presents unique and particular difficulties as application of such methods to the usual hallen type integral equations can yield meaningless results from which no further conclusions should be drawn in the present paper we apply moment methods to properly modified integral equations and obtain much more reliable results we also observe that certain difficulties still remain and discuss them in detail

generalized eigenspace based beamformers the generalized eigenspace based beamformer geib is presented here which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer lcmvb the weight vector of the geib is found by projecting the lcmvb weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix the geib and the lcmvb have the same responses to the desired signal and the interferers however the weight vector of the geib has a smaller norm and generates a lower output noise power an additional advantage of the geib is that the linear constraints can be treated flexibly i e each linear constraint can be chosen to be preserved or not preserved the cost of preserving a linear constraint is to get more output noise power in addition to developing the geib we discuss the effects of imposing linear constraints on the output noise powers of the geib and the lcmvb computer simulations are also presented that demonstrate the merits of the geib

steady state analysis of the generalized sidelobe canceller by adaptive noise cancelling techniques narrow band adaptive noise cancelling techniques are used to study the generalized sidelobe canceller gsc a general form of linearly constrained adaptive beamforming structure in an environment which consists of a look direction signal one jammer and additive receiver noise exact expressions are derived for the wiener solution the steady state output signal to interference plus noise ratio sinr 0 and performance improvement due to adaptation pia defined as the ratio of sinr 0 after adaptation to sinr0 before adaptation these expressions are in terms of the signal directions and power levels an arbitrary array geometry and a general signal blocking matrix next easily evaluated scalar equations for pia are given for two classes of constraints the first is constant gain in the look direction and the second is constant gain plus a main beam zero first derivative in the look direction under the further assumption of an equally spaced line array even simpler equations for pia result and are used to show that for jammers arriving outside the heamwidth between first nulls bwfn region of the unadapted beampattern the introduction of the additional main beam zero first derivative constraint leads to negligible degradation in pia

multichannel post filtering in nonstationary noise environments in this paper we present a multichannel post filtering approach for minimizing the log spectral amplitude distortion in nonstationary noise environments the beamformer is realistically assumed to have a steering error a blocking matrix that is unable to block all of the desired signal components and a noise canceller that is adapted to the pseudo stationary noise but not modified during transient interferences a mild assumption is made that a desired signal component is stronger at the beamformer output than at any reference noise signal and a noise component is strongest at one of the reference signals the ratio between the transient power at the beamformer output and the transient power at the reference noise signals is used to indicate whether such a transient is desired or interfering based on a gaussian statistical model and combined with an appropriate spectral enhancement technique we derive estimators for the signal presence probability the noise power spectral density and the clean signal the proposed method is tested in various nonstationary noise environments compared with single channel post filtering a significantly reduced level of nonstationary noise is achieved without further distorting the desired signal components

on two types of convergence in the method of auxiliary sources the method of auxiliary sources mas is often applied to problems involving an externally illuminated smooth perfect electric conductor pec one seeks to approximately satisfy the boundary condition on the pec surface using auxiliary sources located inside the pec surface usually the underlying auxiliary surface is also smooth and closed the currents on the auxiliary sources mas currents are the initial unknowns once they have been found one can easily determine the field due to them mas field at all points external to the auxiliary surface and in particular at all points external to the pec scatterer we show that in the limit n it is possible to have a convergent mas field together with divergent mas currents and that this phenomenon is accompanied by an abrupt behavior of the limiting value of the mas field we show this possibility through an analytical study of a two dimensional scattering problem involving a circular cylinder in which mas fields and currents can be determined explicitly the analytical study proceeds from first principles it involves fundamental electromagnetics and relatively simple mathematical manipulations numerical results supplement the analytical study and demonstrate the nature of the aforementioned divergence our study sheds light on other aspects of mas in particular it establishes interesting similarities and differences between mas and its continuous version and reveals many similarities between mas currents and numerical solutions of hallen s integral equation with the approximate kernel

robust wideband beamforming with frequency response variation constraint subject to arbitrary norm bounded error traditional robust wideband beamforming is mainly achieved by extending the narrowband robust beamforming methods to the wideband case through frequency sampling with robust constraints imposed on different frequency points separately the resultant beamformer may have different responses at different frequencies causing intolerable distortion to the desired signal to improve the frequency response consistency of the beamformer against arbitrary array manifold errors a novel robust beamformer is proposed with a closed form solution a previously proposed robust beamformer can be considered as its special case

the broad band wiener solution for griffiths jim beamformers the authors treat the problem of finding the wiener filters for a wideband adaptive beamformer explicit expressions are given for the filters and error power spectrum in the frequency domain the expressions are simple to program and give the possibility of investigating superresolution for wideband signals and of determining sufficient lengths of the finite impulse response filters in adaptive arrays the major results are an analytical expression for the broadband array wiener solution given for an arbitrary spectrum for target interference and noise and an approximate analytic expression for the angular 3 db beamwidth for broadband signals

a robust algorithm for adaptive interference cancellation a robust algorithm is introduced for adaptive beamformer in the presence of pointing errors it preserves the desired signal and keeps nice interference nulling simultaneously this advantage is achieved by incorporating spatial derivative constraints with injected noise and pseudo interference the resulted angular beamwidth is insensitive to the input signal to noise ratio

two dimensional highly directive currents on large circular loops properties of idealized two dimensional current distributions on circular loops are investigated analytically via the solution of a constrained optimization problem the directivity in the far field is maximized under a fixed c n t where n is the integral of the square of the current magnitude and t is the total radiated power c enters the ensuing fourier series for the current implicitly through a lagrange multiplier for non negative and large electrical radius ka the directivity and the current are evaluated approximately via combined use of the poisson summation formula and the mellin transform technique as a result a geometrical ray representation for the current is derived for the case of directivities that are slightly larger than that of the uniform distribution the analysis indicates certain advantages of large radiating structures for moderate values of the constraint c in the limit c of oseen s einstein needle radiation an asymptotic formula for the directivity is obtained pos

existence of global smooth solution to the initial boundary value problem for p system with damping abstract this paper is concerned with the initial boundary value problem for the p system with damping we prove the existence of the global smooth solution under the assumption that only the c 0 norm of the derivative of the initial data is sufficiently small while the c 0 norm of the initial data is not necessarily small the proof is based on several key a priori estimates the maximum principle and the characteristic method

adaptive wideband beamforming with frequency invariance constraints a response variation rv element is introduced to control the consistency of an adaptive wideband beamformer s response over the frequency range of interest by incorporating the rv element into the linearly constrained minimum variance lcmv beamformer we develop a novel linearly constrained beamformer with an improved output signal to interference plus noise ratio sinr compared to both the traditional formulation and the eigenvector based formulation due to an increased number of degrees of freedom for interference suppression in addition two novel wideband beamformers robust against look direction estimation errors are also proposed as a further application of the rv element one is designed by imposing a constraint on the rv element and simultaneously limiting the magnitude response of the beamformer within a pre defined angle range at a reference frequency the other one is obtained by combining the rv element and the worst case performance optimization method both of them are reformulated in a convex form as the second order cone soc programming problem and solved efficiently using interior point method compared with the original robust methods a more efficient and effective control over the beamformer s response at the look direction region is achieved with an improved overall performance

highly directive current distributions general theory a theoretical scheme for studying the properties of localized monochromatic and highly directive classical current distributions in two and three dimensions is formulated and analyzed for continuous current distributions it is shown that maximizing the directivity d in the far field while constraining c5n t where n is the integral of the square of the magnitude of the current density and t is proportional to the total radiated power leads to a fredholm integral equation of the second kind for the optimum current this equation is a useful analytical tool for studying currents that produce optimum directivities above the directivity of a uniform distribution various consequences of the present formulation are examined analytically for essentially arbitrary geometries of the current carrying region in particular certain properties of the optimum directivity are derived and differences between the continuous and discrete cases are pointed out when c the directivity tends to infinity monotonically in accord with oseen s einstein needle radiation s1063 651x 98 02108 4

system identification using chirp signals and time variant filters in the joint time frequency domain we propose a novel method to identify an unknown linear time invariant lti system in low signal to noise ratio snr environment the method is based on transmitting chirp signals for the transmitter and using linear time variant filters in the joint time frequency tf domain for the receiver to reduce noise before identification due to the tf localization property of chirp signals a large amount of additive white noise can be reduced and therefore the snr before identification can be significantly increased this however cannot be achieved in the conventional methods where pseudo random signals are used and therefore noise reduction techniques do not apply our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low snr environment this paper provides a good application of time frequency analysis and synthesis

nonparametric identification of linear dynamic errors in variables systems the present work handles the nonparametric identification of linear dynamic systems within an errors in variables framework where the input is arbitrary and both the input and output disturbing noises are white with unknown variances using the property that the frequency response function and the system leakage term can be locally approximated very well by a low order degree polynomial a frequency domain estimator is developed which gives consistent estimates for the frequency response function and the input output noise variances the consistency and uniqueness of the estimator are theoretically analyzed under mild conditions and uncertainty bounds are also provided the proposed method is finally validated on a simulated linear dynamic system

on solutions of the wave equation with a sublinear dissipative term the existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation utt u ut f in r or r with the boundary condition u 0 are proved where is a bounded domain in rn and v is a sublinear function say v k0 v rv k0 0 0 r 1

on the damped nonlinear evolution equation wtt σ w xx ywt abstract initial boundary value problems for the damped nonlinear wave equation wtt w xx ywt arise in several areas of applied mathematics and in particular in studies of shearing flow in a nonlinear viscoelastic fluid the problems of global existence and nonexistence of smooth solutions have been extensively studied in the strictly hyperbolic case e 0 r1 as well as in the case where 0 0 and the initial data are chosen so small that w 0 for as long as a smooth solution w x t exists in this paper the global nonexistence problem is studied for the cases 0 0 and 0 0 but