existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

the stability for a one dimensional wave equation with nonlinear uncertainty on the boundary abstract in this work we are concerned with the boundary stabilization of a one dimensional wave equation subject to boundary nonlinear uncertainty the nonlinear uncertainty is first estimated in terms of the output and then canceled by its estimates we show that this strategy works well when the derivative of the uncertainty is bounded

local error estimates for some petrov galerkin methods applied to strongly elliptic equations on curves on etudie les proprietes de convergence locales de quelques methodes de petrov galerkin appliquees aux equations fortement elliptiques sur des courbes regulieres du plan on etablit des estimations d erreurs locales pour une grande echelle de normes de sobolev

a posteriori error control in adaptive qualocation boundary element analysis for a logarithmic kernel integral equation of the first kind sobolev slobodeckij norms on small overlapping domains of two neighboring elements serve as a posteriori error estimators and mesh refining indicators in adaptive boundary element methods this paper is concerned with two error estimators eta f and mu f the first variant eta f is efficient and the second mu f is reliable that is up to multiplicative constants and numerical quadrature errors they are lower or upper error bounds faermann recently established reliability and efficiency of eta f for the galerkin boundary element method and considered mu f this work approaches the two estimators eta f le mu f for the galerkin qualocation and collocation boundary element methods for a single layer operator integral equation of the first kind upper and lower bounds are established theoretically and validated numerically numerical experiments support the estimators accuracies and the efficiencies of proposed adaptive mesh refining algorithms even in energy norms for qualocation and collocation schemes difficulties for alpha le 1 2 are caused by the lack of a sobolev embedding h alpha gamma hookrightarrow mathcal c gamma hence for the latter schemes equivalence of error and estimators in h alpha 1 gamma can be proven only for alpha 1 2 numerical evidence conjectures equivalence for alpha 1 2 as well

blow up and critical exponents for nonlinear hyperbolic equations we prove nonexistence results for the cauchy problem for the abstract hyperbolic equation in a banach space x utt f u t 0 u 0 u0 ut 0 u1 where f x r is a c1 function several applications to the second and higher order hyperbolic equations with local and nonlocal nonlinearities are presented we also describe an approach to kato s and john s critical exponents for the semilinear equations ut u b x t u p p 1 which are responsible for phenomena of stability unstability blow up and asymptotic behaviour

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

additivity of auditory masking using gaussian shaped tones both temporal and spectral masking have been studied extensively in the literature mostly they have been regarded as separate phenomena very little is known about the interaction between these two effects i e masking in the time frequency domain data on the time frequency spread of masking evoked by a single gaussian shaped tone pulse are presented in an accompanying study at the same conference necciari et al the current study gathers data on the additivity of masking by up to four approximately equally effective gaussian maskers erb 600 hz separated either along the time or the frequency axis for temporal separation the amount of masking increases with the number of maskers with excess masking exceeding linear additivity of up to 25 db for frequency separation preliminary data excess masking amounts up to 15 db and the higher frequency masker relative to the target contributes more to the additivity than the lower frequency maskers experiments with multiple maskers combining both temporal and frequency separation are underway combined with the single maker data these data may serve as a basis for modeling time frequency masking effects in complex signals work partly supported by oead wtz project amadeus and anr

stability analysis of the anti stable heat equation with uncertain disturbance on the boundary abstract in this paper we study the stability of the anti stable 1 d heat equation with uncertain disturbance on the boundary we first estimate the disturbance in terms of the output then we design some control strategy to stabilize the anti stable system

models of the additivity of masking three models of masking additivity are reviewed which are referred to as the high compression model m j penner j acoust soc am 67 608 616 1980 m j penner and r m shiffrin j acoust soc am 67 617 627 1980 the power law model r a lutfi j acoust soc am 73 262 267 1983 80 422 428 1986 and the modified power law model with compressed internal noise humes et al j acoust soc am 83 188 202 1988 while the high compression model was derived from data for two or more nonsimultaneous maskers and the power law model was derived from data for two or more simultaneous maskers the modified power law model can be applied to both cases the modified power law model assumes that the threshold in quiet is equivalent to a masked threshold resulting from an internal noise that is continually present additional assumptions concern the interaction of two maskers prior to the addition of the masking effects most of the data on the additivity of masking are well described b

active disturbance rejection control based on weighed moving average state observer abstract in this work we are concerned with the boundary stabilization of a one dimensional anti stable wave equation corrupted by a boundary disturbance we firstly propose by weighed moving average technique a state observer to make an estimation of the disturbance secondly we design a control by the active disturbance rejection strategy to stabilize the system

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term the wave equation with a source term is considered utt u u uin 0 we prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback ut acting on the boundary provided that has necessarily not a polynomial growth near the origin to obtain the existence of global solutions we make use of the potential well method combined with the faedo galerkin procedure and constructing a special basis furthermore we prove that the energy of the system decays uniformly to zero and we obtain an explicit decay rate estimate adapting the ideas of lasiecka and tataru differential integral equations 6 3 1993 507 and patrick martinez esain control optimisation calc var 4 1999 419 the resulting problem generalizes martinez results and complements the works of lasiecka and tataru 1993 and vitillaro glasgow math j 44 2002 375

intensity discrimination of gaussian windowed tones indications for the shape of the auditory frequency time window the just noticeable difference in intensity jnd i was measured for 1 khz tones with a gaussian shaped envelope as a function of their spectro temporal shape the stimuli with constant energy and a constant product of bandwidth and duration ranged from a long duration narrow band tone to a short duration broadband click the jnd i was measured in three normal hearing listeners at sensation levels of 0 10 20 and 30 db in 35 db a spl pink noise at intermediate sensation levels jnd i depends on the spectro temporal shape at the extreme shapes tones and clicks intensity discrimination performance is best whereas at intermediate shapes the jnd i is larger similar results are observed at a higher overall sound level and at a higher carrier frequency the maximum jnd i is observed for stimuli with an effective bandwidth of about 1 3 octave and an effective duration of 4 ms at 1 khz 1 ms at 4 khz a generalized multiple window model is proposed that assumes that the spectro temporal domain is partitioned into internal auditory frequency time windows the model predicts that intensity discrimination thresholds depend upon the number of windows excited by a signal jnd i is largest for stimuli covering one window

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

a note on the boundary stabilization of the wave equation we study the energy decay rates of the wave equation in a domain where boundary damping is present we generalize the geometrical conditions obtained earlier in j math purer appl 58 1979 pp 249 273 by using some more general multipliers of strauss comm pure appl math 28 1975 pp 265 278 the interaction between distributed damping and boundary damping is discussed a regulator problem is also formally discussed by the synthesis method

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

on nonlinear wave equations with degenerate damping and source terms in this article we focus on the global well posedness of the differential equation u tt u u k j u t u p 1 u in x 0 t where j is a sub differential of a continuous convex function j under some conditions on j and the parameters in the equations we obtain several results on the existence of global solutions uniqueness nonexistence and propagation of regularity under nominal assumptions on the parameters we establish the existence of global generalized solutions with further restrictions on the parameters we prove the existence and uniqueness of a global weak solution in addition we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent p is greater than the critical value k m and the initial energy is negative we also address the issue of propagation of regularity specifically under some restriction on the parameters we prove that solutions that correspond to any regular initial data such that u 0 h 2 h 1 0 u 1 h 1 0 are indeed strong solutions

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

uniform decay rate estimates for schrodinger and plate equations with nonlinear locally distributed damping on a compact n dimensional riemannian manifold m g we establish uniform decay rate estimates for the linear schrodinger and plate equations subject to an internal nonlinear damping locally distributed on the manifold our approach can be also employed for other equations provided that inverse inequality for the linear model occurs in the particular case of the wave equation where the well known geometric control condition gcc is equivalent to the observability inequality our method generalizes the results due to cavalcanti et al 2010 2009 9 10 regarding the optimal choice of dissipative regions

the application of cubic trigonometric b spline to the numerical solution of the hyperbolic problems in this paper a collocation finite difference scheme based on new cubic trigonometric b spline is developed and analyzed for the numerical solution of a one dimensional hyperbolic equation wave equation with non local conservation condition the usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric b spline is utilized as an interpolation function in the space dimension the scheme is shown to be unconditionally stable using the von neumann fourier method the accuracy of the proposed scheme is tested by using it for several test problems the numerical results are found to be in good agreement with known exact solutions and with existing schemes in literature

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

mathematical foundation of adaptive boundary element methods abstract in this paper we review some mathematical aspects of adaptive boundary element methods in brief and give some a posteriori local error estimates for the h version and the p version

output feedback stabilization of an unstable wave equation with general corrupted boundary observation we consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance we adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback by the approach the disturbance is first estimated by a relatively independent estimator it is then canceled in the feedback loop as a result the control law can be designed almost as that for the system without disturbance we show that with a time varying gain properly designed the observer driven by the disturbance estimator is convergent and that all subsystems in the closed loop are asymptotically stable in the energy state space we also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction

adaptive boundary element methods for strongly elliptic integral equations integral operators are nonlocal operators the operators defined in boundary integral equations to elliptic boundary value problems however are pseudo differential operators on the boundary and therefore provide additional pseudolocal properties these allow the successful application of adaptive procedures to some boundary element methods in this paper we analyze these methods for general strongly elliptic integral equations and obtain a posteriori error estimates for boundary element solutions we also apply these methods to nodal collocation with odd degree splines some numerical examples show that these adaptive procedures are reliable and effective