on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

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

uniform stabilization of the damped cauchy ventcel problem with variable coefficients and dynamic boundary conditions in this paper the uniform stabilization of the cauchy ventcel problem with variable coefficients is considered and the uniform energy decay rate for the problem is established by riemannian geometry methods

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

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

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

asymptotic stability of the wave equation on compact surfaces and locally distributed damping a sharp result this paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping described by u tt m u x g u t 0 on m 0 where m c r 3 is a smooth oriented embedded compact surface without boundary denoting by g the riemannian metric induced on m by r 3 we prove that for each 0 there exist an open subset v c m and a smooth function f m r such that meas v meas m e hessf g on v and inf f x 0 x v in addition we prove that if x a o 0 on an open subset m c m which contains m v and if g is a monotonic increasing function such that k s g s k s for all s 1 then uniform and optimal decay rates of the energy hold

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

the null timelike boundary problem for maxwell s equations in minkowski space we consider maxwell s equations in an exterior region of minkowski space with boundary conditions specified on a timelike cylinder and on a characteristic cone we prove gauge fixing results and u

limiting properties of the least squares estimator of a continuous threshold autoregressive model the continuous threshold autoregressive model is a sub class of the threshold autoregressive model subject to the requirement that the piece wise linear autoregressive function be continuous everywhere in contrast with the discontinuous case it is shown that under suitable regularity conditions the conditional least squares estimator of the parameters including the threshold parameter is root n consistent and asymptotically normally distributed the theory is illustrated by a simulation study and is applied to the quarterly u s unemployment rates

blow up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities abstract we investigate a hyperbolic pde modeling wave propagation in viscoelastic media under the influence of a linear memory term of boltzmann type and a nonlinear damping modeling friction as well as an energy amplifying supercritical nonlinear source u t t k 0 u 0 k s u t s d s u t m 1 u t u p 1 u in 0 t u x t u 0 x t in 0 where is a bounded domain in r 3 with a dirichlet boundary condition the relaxation kernel k is monotone decreasing and k 1 we study blow up of solutions when the source is stronger than dissipations i e p max m k 0 under two different scenarios first the total energy is negative and the second the total energy is positive with sufficiently large quadratic energy this manuscript is a follow up work of the paper 30 in which hadamard well posedness of this equation has been established in the finite energy space the model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite time memory

stabilization of wave and plate like equations with nonlinear dissipation on the boundary abstract in this paper we consider second order in time equations of petrovsky type wave and plate like with nonlinear dissipative boundary conditions under certain geometric conditions imposed on the domain the results on asymptotic behavior of the solutions are established

local m estimation with discontinuous criterion for dependent and limited observations this paper examines asymptotic properties of local m estimators under three sets of high level conditions these conditions are sufficiently general to cover the minimum volume predictive region conditional maximum score estimator for a panel data discrete choice model and many other widely used estimators in statistics and econometrics specifically they allow for discontinuous criterion functions of weakly dependent observations which may be localized by kernel smoothing and contain nuisance parameters whose dimension may grow to infinity furthermore the localization can occur around parameter values rather than around a fixed point and the observation may take limited values which leads to set estimators our theory produces three different nonparametric cube root rates and enables valid inference for the local m estimators building on novel maximal inequalities for weakly dependent data our results include the standard cube root asymptotics as a special case to illustrate the usefulness of our results we verify our conditions for various examples such as the hough transform estimator with diminishing bandwidth maximum score type set estimator and many others

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

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

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

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

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

consistency and limiting distribution of the least squares estimator of a threshold autoregressive model it is shown that under some regularity conditions the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent the limiting distribution of the least squares estimator is derived it is shown that the estimator of the threshold parameter is n consistent and its limiting distribution is related to a compound poisson process

wave equation with porous nonlinear acoustic boundary conditions generates a well posed dynamical system we consider a structural acoustic wave equation with nonlinear acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with boundary conditions on the interface we prove wellposedness in the hadamard sense for strong and weak solutions the main tool used in the proof is the theory of nonlinear semigroups we present the system of partial differential equations as a suitable cauchy problem dw dt aw though the operator a is not maximally dissipative we are able to show that it is a translate of a maximally dissipative operator the obtained semigroup solution is shown to satisfy a suitable variational equality thus giving weak solutions to the system of pdes the results obtained i dispel the notion that the model does not generate semigroup solutions ii provide treatment of nonlinear models and iii provide existence of a correct state space which is invariant under the flow thus showing that physical model under consideration is a dynamical system the latter is obtained by eliminating compatibility conditions which have been assumed in previous work on the linear case

test inversion bootstrap confidence intervals summary in this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals in the presence of nuisance parameters we show that the coverage error of such intervals is o n 112 which may be reduced to o n 1 if a studentized statistic is used we present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence interval for the doseresponse parameter in models of the japanese atomic bomb survivors data

quasilinear hyperbolic 2 2 systems with a free damping boundary condition we consider a quasilinear system of equations for two functions u x t v x t and a boundary function s t

robust inference for threshold regression models abstract this paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump nesting previous works that assume either continuity or discontinuity at the threshold we find that the parameter values under the kink restriction are irregular points of the hessian matrix destroying the asymptotic normality and inducing the cube root convergence rate for the threshold estimate however we are able to obtain the same asymptotic distribution as hansen 2000 for the quasi likelihood ratio statistic for the unknown threshold we propose to construct confidence intervals for the threshold by bootstrap test inversion finite sample performances of the proposed procedures are examined through monte carlo simulations and an economic empirical application is given

stability of parabolic problems with nonlinear wentzell boundary conditions abstract of concern is the nonlinear uniformly parabolic problem u t div a u u 0 x f x u t a u x u q lb u 0 for x r n and t 0 the last equation holds on the boundary here a a i j x i j is a real hermitian uniformly positive definite n n matrix c with 0 r r q 0 lb is the laplace beltrami operator on the boundary and a u is the conormal derivative of u with respect to a and everything is sufficiently regular the solution of this wellposed problem depends continuously on the ingredients of the problem namely a q f this is shown using semigroup methods in g m coclite a favini g r goldstein j a goldstein s romanelli continuous dependence on the boundary parameters for the wentzell laplacian semigroup forum 77 1 2008 101 108 here we prove explicit stability estimates of the solution u with respect to the coefficients a q and the initial condition f moreover we cover the singular case of a problem with q 0 which is approximated by problems with positive q

global nonexistence for a semilinear wave equation with nonlinear boundary dissipation in this paper we consider the following problem ytt yxx yt y p 1y x t 0 l 0 t y 0 t 0 t 0 t yx l t y l t yt l t m 1yt l t 0 t 0 t y x 0 y0 x yt x 0 y1 x x 0 l where 0 l is a bounded open interval in r p 1 and m 1 we are interested in the interaction between the boundary damping yt l t m 1yt l t and the interior source y t p 1y t under some appropriate assumptions on the initial data two blow up results with positive initial energy are established furthermore we obtain that the solutions blow up if p or y0 l is sufficiently large

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

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

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping we study wave equations with acoustic boundary conditions where only one memory damping acts on the acoustic boundary under some conditions on the memory kernel polynomial energy decay rates are established by using higher order energy estimates among some other techniques

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

change point in stochastic design regression and the bootstrap in this paper we study the consistency of dierent bootstrap procedures for constructing condence intervals cis for the unique jump discontinuity change point in an otherwise smooth regression function in a stochastic design setting this problem exhibits nonstandard asymptotics and we argue that the standard bootstrap procedures in regression fail to provide valid condence intervals for the change point we propose a version of smoothed bootstrap illustrate its remarkable nite sample performance in our simulation study and prove the consistency of the procedure the m out of n bootstrap procedure is also considered and shown to be consistent we also provide sucient conditions for any bootstrap procedure to be consistent in this scenario

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

estimates for first order homogeneous linear characteristic problems an algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first order homogeneous linear characteristic problems is derived estimates of such kind ensure the stability of the solutions under small variations of the data characteristic problems that satisfy this criterion are in a sense manifestly well posed

a smoothed least squares estimator for threshold regression models abstract we propose a smoothed least squares estimator of the parameters of a threshold regression model our model generalizes that considered in hansen 2000 sample splitting and threshold estimation econometrica 68 575 603 to allow the thresholding to depend on a linear index of observed regressors thus allowing discrete variables to enter we also do not assume that the threshold effect is vanishingly small our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters

global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation abstract in this paper we consider the long time behavior of solutions of the initial value problem for semilinear wave equations of the form formula

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

subsampling inference in threshold autoregressive models this paper discusses inference in self exciting threshold autoregressive setar models of main interest is inference for the threshold parameter it is well known that the asymptotics of the corresponding estimator depend upon whether the setar model is continuous or not in the continuous case the limiting distribution is normal and standard inference is possible in the discontinuous case the limiting distribution is non normal and it is not known how to estimate it consistently we show that valid inference can be drawn by the use of the subsampling method moreover the method can even be extended to situations where the dis continuity of the model is unknown in this case the inference for the regression parameters of the model also becomes difficult and subsampling can be used again in addition we consider an hypothesis test for the continuity of a setar model a simulation study examines small sample performance and an application illustrates how the proposed methodology works in practice

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

estimates for the characteristic problem of the first order reduction of the wave equation we calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order in terms of the free data prescribed on two transverse surfaces one of which is characteristic estimates of such kind ensure the stability of the solutions under small variations of the data similar estimates exist for the derivatives of the solution as well

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

energy decay rate for a von karman system with a boundary nonlinear delay term abstract in this paper we show the energy decay rate for a von karman system with a boundary nonlinear delay term this work is devoted to investigate the influence of kernel function g and the effect of the boundary nonlinear term 1 u t t m 1 u t t a boundary nonlinear time delay term 2 u t t m 1 u t t and prove energy decay rates of solutions when g do not necessarily decay exponentially and the boundary condition has a time delay

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time varying delay in the boundary feedback abstract a variable coefficient wave equation with acoustic boundary conditions and a time varying delay in the boundary feedback is considered applying the riemannian geometry method we show that the decay rates of the nonlinear system with a time varying delay are described by solutions to a first order ode

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

stabilization of the wave equation with localized nonlinear damping abstract we prove some decay estimates of the energy of the wave equation in a bounded domain the damping is nonlinear and is effective only in a neighborhood of a suitable subset of the boundary the method of proof is direct and is based on the multipliers technique on some integral inequalities due to haraux and komornik and on a judicious idea of conrad and rao

invariance principles for mixing sequences of random variables in this note we prove weak invariance principles for some classes of mixing sequences of l 2 integrable random variables under the condition that the variance of the sum of n random variables is asymptotic to sigma 2n where sigma 2 0 one of the results is simultaneously an extension to nonstationary case of a theorem of ibragimov and an improvement of the varphi mixing rate used by mcleish in his invariance principle for nonstationary varphi mixing sequences

global nonexistence theorems for a class of evolution equations with dissipation we study abstract evolution equations with nonlinear damping terms and source terms including as a particular case a nonlinear wave equation of the type ba cl u tt delta u b u t m 2 u t c u p 2 u t x in 0 t times omega 6pt u t x 0 t x in 0 t times partial omega 6pt u 0 cdot u 0 in h 0 1 omega quad u t 0 cdot v 0 in l 2 omega es ea where 0 p 2 m 1 we prove a global nonexistence theorem for positive initial value of the energy when 1 1

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

identification and estimation of treatment effects with a regression discontinuity design the regression discontinuity rd data design is a quasi experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables this data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment in the first application and discussion of the rd method thistlethwaite and campbell 1960 study the effect of student scholarships on career aspirations using the fact that awards are only made if a test score exceeds a threshold more recently van der klaauw 1997 estimates the effect of financial aid offers on students decisions to attend a particular college taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students grade point average and sat score angrist and lavy 1999 estimate the effect of class size on student test scores taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level finally black 1999 uses an rd approach to estimate parents willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries regression discontinuity methods have potentially broad applicability in economic research because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method although there have been several discussions and applications of rd methods in the literature important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions here we show that identifying conditions invoked in previous applications of rd methods are often overly strong and that treatment effects can be nonparametrically identified under an rd design by a weak functional form restriction the restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism we also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the wald estimator as an rd estimator

cube root asymptotics we establish a new functional central limit theorem for empirical processes indexed by classes of functions in a neighborhood of a fixed parameter point an n 1 3 rescaling of the parameter is compensated for by an n 2 3 rescaling of the empirical measure resulting in a limiting gaussian process by means of a modified continuous mapping theorem for the location of the maximizing value we deduce limit theorems for several statistics defined by maximization or constrained minimization of a process derived from the empirical measure these statistics include the short rousseeuw s least median of squares estimator manski s maximum score estimator and the maximum likelihood estimator for a monotone density the limit theory depends on a simple new sufficient condition for a gaussian process to achieve its maximum almost surely at a unique point

global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions abstract we consider a quasilinear wave equation u t t u t d i v u 2 u d i v u t 2 u t a u t m 2 u t 1 u t x t 2 u t x t b u p 2 u a b 0 associated with initial and dirichlet boundary conditions at one part and acoustic boundary conditions at another part respectively we prove under suitable conditions on m p and for negative initial energy a global nonexistence of solutions