exponential decay for a von karman equations with memory in this paper we consider a von karman equations with memory term we show an exponential decay result of solutions under weaker assumption than the ones frequently used in the literature in particular the kernel we are considering is not necessarily exponentially decaying to zero as was assumed before

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

the cauchy problem in one dimensional nonlinear viscoelasticity abstract the initial value problem for a nonlinear hyperbolic volterra equation which models the motion of an unbounded viscoelastic bar is studied under physically motivated assumptions the existence of a unique globally defined classical solution is established provided the initial data are sufficiently smooth and small boundedness and asymptotic behavior are also discussed this analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels

a decay result to a viscoelastic problem in rn with an oscillating kernel in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for not necessarily decreasing oscillating relaxation function the decay of the first energy of solutions is polynomial the proof relies on some appropriately chosen functionals the combination of which satisfies a certain integral inequality

general decay of solutions of a viscoelastic equation abstract in this paper we consider the following viscoelastic equation u t t u 0 t g t u d 0 in a bounded domain and establish a general decay result which is not necessarily of exponential or polynomial type this work generalizes and improves earlier results in the literature

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

upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation abstract for a smooth bounded domain r n n 3 and e a real parameter consider the hyperbolic equation eu tt u t u u g in with dirichlet boundary conditions under certain conditions on this equation has a compact attractor a e in h 0 1 l 2 for e 0 the parabolic equation also has a compact attractor which can be naturally embedded into a compact set a 0 in h 0 1 l 2 it is shown that for any neighborhood u of a 0 the set a e u for e small

uniform decay in viscoelasticity for kernels with small non decreasingness zones abstract we consider a viscoelastic problem with a relaxation function which may be strictly increasing in some sub intervals that is we go beyond the zero which was a bound for the derivative of the kernel in the previous works it is proved that we have different types of decay rates including the exponential one provided that the rate and or the non decreasingness zone including the flat zone is small enough in a certain sense

energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions in this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions motivated by results of gerbi and said houari 2011 2008 li and zhao 2011 liu and chen 2016 wu etal 2010 and lu etal 2011 we intend to study the energy decay rates for problem 1 1 1 6 by using the perturbed energy method and riemannian geometry method we obtained general energy decay rates

on a large class of kernels yielding exponential stability in viscoelasticity in this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity the conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated namely the smallness of the kernels is replaced by the smallness of the set where the kernel is flat this work extends previous works and improves in particular a recent result by pata 16 this is established by introducing two lemmas an idea due to pata and using the energy method

going off grid computationally efficient inference for log gaussian cox processes this paper introduces a new method for performing computational inference on log gaussian cox processes the likelihood is approximated directly by making novel use of a continuously specified gaussian random field we show that for sufficiently smooth gaussian random field prior distributions the approximation can converge with arbitrarily high order while an approximation based on a counting process on a partition of the domain only achieves first order convergence the given results improve on the general theory of convergence of the stochastic partial differential equation models introduced by lindgren et al 2011 the new method is demonstrated on a standard point pattern data set and two interesting extensions to the classical log gaussian cox process framework are discussed the first extension considers variable sampling effort throughout the observation window and implements the method of chakraborty et al 2011 the second extension constructs a log gaussian cox process on the world s oceans the analysis is performed using integrated nested laplace approximation for fast approximate inference

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

optimality of energy estimates for the wave equation with nonlinear boundary velocity feedbacks we consider the wave equation damped by a nonlinear boundary velocity feedback q ut first we consider the case where q has a linear growth at infinity we prove that the usual decay rate estimates proved by nakao differential integral equations 8 1995 pp 681 688 haraux and zuazua arch rational mech anal 100 1988 pp 191 206 conrad leblond and marmorat in proceedings of the fifth international federation of automatic control symposium on control of distributed parameter systems perpignan 1989 pp 101 116 zuazua siam j control optim 28 1990 pp 466 477 and komornik in control and estimation of distributed parameter systems nonlinear phenomena internat ser numer math 118 birkhauser basel 1994 pp 253 266 when q has a polynomial behavior at zero and by the second author esaim control optim calc var 4 1999 pp 419 444 in the general case are in fact optimal in one space dimension more generally we prove that the energy decays exactly like the solution of an explicit and simple ordinary differential equation next we study the problem when q is bounded at infinity we prove that strong solutions decay exponentially to zero and we exhibit a sequence of weak solutions for which the associated energy decays to zero at infinity as slowly as the iterated logarithms go to infinity at infinity

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

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

singular perturbation for volterra equations of convolution type under the assumption that a is the generator of a twice integrated cosine family and k is a scalar valued kernel we solve the singular perturbation problem e e e 2u e t u e t au e t k au e t f e t t 0 e 0 when e 0 for the integrodifferential equation e w t aw t k aw t f t t 0 on a banach space if the kernel k verifies some regularity conditions then we show that problem e e has a unique solution u e t for each small e 0 moreover u e t converges as e 0 to the unique solution u t of equation e

spatiotemporal prediction for log gaussian cox processes space time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems we describe a flexible class of space time point processes our models are cox processes whose stochastic intensity is a space time ornstein uhlenbeck process we develop moment based methods of parameter estimation show how to predict the underlying intensity by using a markov chain monte carlo approach and illustrate the performance of our methods on a synthetic data set

general stability result for viscoelastic wave equations in this paper we consider a viscoelastic equation and establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity our result allows a wider class of relaxation functions and improves earlier results in the literature

the hyperbolic singular perturbation problem an operator theoretic approach abstract we study the convergence of solutions of e2u t u t e2a b u t to solutions of u t bu t as e 0 where a and b are linear unbounded operators in a banach space

on the uniform decay in viscoelastic problems in rn in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for an exponentially decaying relaxation function the decay of the first energy of solution is polynomial the finite speed propagation is used to compensate for the lack of poincare s inequality in r n

exact bayesian inference in spatiotemporal cox processes driven by multivariate gaussian processes summary we present a novel inference methodology to perform bayesian inference for spatiotemporal cox processes where the intensity function depends on a multivariate gaussian process dynamic gaussian processes are introduced to enable evolution of the intensity function over discrete time the novelty of the method lies on the fact that no discretization error is involved despite the non tractability of the likelihood function and infinite dimensionality of the problem the method is based on a markov chain monte carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model a particular choice of the dominating measure to obtain the likelihood function is shown to be crucial to devise a valid markov chain monte carlo algorithm the models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions because of careful characterization of its components the models also enable the inclusion of regression covariates and or temporal components to explain the variability of the intensity function these components may be subject to relevant interaction with space and or time real and simulated examples illustrate the methodology followed by concluding remarks

the bloch wave operator generalizations and applications part i the time independent case this is part 1 of a two part review on wave operator theory and methods the basic theory of the time independent wave operator is presented in terms of partitioned matrix theory for the benefit of general readers with a discussion of the links between the matrix and projection operator approaches the matrix approach is shown to lead to simple derivations of the wave operators and effective hamiltonians of lowdin bloch des cloizeaux and kato as well as to some associated variational forms the principal approach used throughout stresses the solution of the nonlinear equation for the reduced wave operator leading to the construction of the effective hamiltonians of bloch and of des cloizeaux several mathematical techniques which are useful in implementing this approach are explained some of them being relatively little known in the area of wave operator calculations the theoretical discussion is accompanied by several specimen numerical calculations which apply the described techniques to a selection of test matrices taken from the previous literature on wave operator methods the main emphasis throughout is on the use of numerical methods which use iterative or perturbation algorithms with simple pade approximant methods being found sufficient to deal with most of the cases of divergence which are encountered the use of damping factors and relaxation parameters is found to be effective in stabilizing calculations which use the energy dependent effective hamiltonian of lowdin in general the computations suggest that the numerical applications of the nonlinear equation for the reduced wave operator are best carried out with the equation split into a pair of equations in which the bloch effective hamiltonian appears as a separate entity the presentation of the theoretical and computational details throughout is accompanied by references to and discussion of many works which have used wave operator methods in physics chemistry and engineering some of the techniques described in this part 1 will be further extended and applied in part 2 of the review which deals with the changes which are required to extend wave operator theory to the case of a time dependent hamiltonian such as that which describes the interaction of a laser pulse with an atom or molecule

on convexity for energy decay rates of a viscoelastic equation with boundary feedback abstract in this paper we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

arbitrary decay rates of energy for a von karman equation of memory type in this paper we consider a von karman equation of memory type u t t 2 u 0 t g t s 2 u s d s u f u with clamped boundary condition we establish a decay result of solutions without imposing the usual relation between a kernel function g and its derivative this result generalizes earlier ones to an arbitrary rate of decay which is not necessarily of an exponential or polynomial decay

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

hyperbolic singular perturbations for integrodifferential equations we study the convergence of solutions email protected 2u t e u t e e 2a b u t e email protected 0 tk t s e 2a b u s e ds f t e t 0 u 0 e u 0 e u 0 e u 1 e to solutions ofw t bw t email protected 0 tk t s bw s ds f t t 0 w 0 w 0 when e 0 here a and b are linear unbounded operators in a banach space x k t is a linear bounded operator for each t 0 in x and f t e and f t are given x valued functions our result extends the studies in fattorini j diff eq 70 1987 1 for equations without the integral term and in liu proc am math soc 122 1994 791 for parabolic singular perturbation problems

arbitrary decays in linear viscoelasticity it is by now well known that a necessary condition for the exponential polynomial decay of the energy of a problem arising in viscoelasticity is that the kernel which appears in the memory term itself be of exponential polynomial type by a kernel of exponential polynomial type we mean that the product of this kernel with an exponential polynomial function is summable some researchers have started from this condition to seek other sufficient conditions ensuring exponential or polynomial decay of the energy in this work we generalize these works to an arbitrary decay not necessarily of an exponential or polynomial rate

a singular perturbation of the heat equation with memory in this paper we consider a hyperbolic equation with a memory term in time which can be seen as a singular perturbation of the heat equation with memory the qualitative properties of the solutions of the initial boundary value problems associated with both equations are studied we propose numerical methods for the hyperbolic and parabolic models and their stability properties are analyzed finally we include numerical experiments illustrating the performance of those methods

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

energy decay rates via convexity for some second order evolution equation with memory and nonlinear time dependent dissipation abstract the stabilization of the following abstract integro differential equation u t a u t 0 t g t s a u s d s q t u t f u t is investigated we establish the general decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function g without imposing any restrictive growth assumption on the damping at the origin and strongly weakening the usual assumption of the relaxation function g our approach is based on the multiplier method and make use of some properties of the convex functions these decay results can be applied to various concrete models we shall study some examples to illustrate our result

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

singular perturbations of integro differential equations abstract we study the singular perturbation problem e 2 u t u t au t k au t f t t 0 0 for the integro differential equation e w t aw t k aw t f t t 0 in a banach space when 0 we assume that a is the generator of a strongly continuous cosine family then under some regularity conditions on the scalar valued kernel k we show that problem e has a unique solution u t for each small 0 moreover u t converges to u t as 0 the unique solution of equation e

moore gibson thompson equation with memory part ii general decay of energy abstract we study a temporally third order moore gibson thompson equation with a memory term previously it was known that in non critical regime the global solutions exist and the energy functionals decay to zero more precisely it is known that the energy has exponential decay if the memory kernel decays exponentially the current work is a generalization of the previous one part i in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does exponentially or not

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

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

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

long time numerical solution of a parabolic equation with memory long time stability and convergence properties of two time discreti zation methods for an integro differential equation of parabolic type are studied the methods are based on the standard backward euler and second order back ward differencing methods the memory term is approximated by a quadrature rule with emphasis on such rules with reduced computational memory require ments discretization of the spatial partial differential operators by the finite element method is also considered

iterative eigenvalue method using the bloch wave operator formalism with pade approximants and absorbing boundaries we present an iterative method for calculating eigenvalues and eigenvectors of large non hermitian matrices the method uses an iterative procedure to solve the basic bloch equation h ensuremath omega ensuremath omega h ensuremath omega of wave operator theory it involves nonlinear transformations such as the translation of diagonal matrix elements in the complex plane and the use of pad e approximants to treat the strongly coupled states which constitute an intermediate space around the model space in the particular case of floquet eigenstates the further step of adding time dependent absorbing boundaries significantly improves the convergence properties of the iterative calculations

integro differential equations of hyperbolic type with positive definite kernels abstract the main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in hilbert spaces for kernels that decay exponentially at infinity and possess strongly positive definite primitives the exponential stability of weak solutions is obtained in the energy norm it is also shown that this theory applies to several examples of kernels with possibly variable sign and to a problem in nonlinear viscoelasticity

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping abstract in this paper we consider the uniform decay estimates of solutions for the viscoelastic wave equation u t t 0 u 0 t g t s div a x u s d s b x h u t 0 in 0 under weak assumptions on the functions g h and f we prove the energy functional decays exponentially or polynomially to zero as the time goes to infinity by introducing brief lyapunov functions and precise priori estimates

uniform decay of solutions for a quasilinear system of viscoelastic equations abstract in this paper we consider a system of two coupled quasilinear viscoelastic equations in canonical form with dirichlet boundary condition we use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay with exponential and polynomial rates of the solutions energy which extends some existing results for a single equation to the case of a coupled system

exponential energy decay of solutions of viscoelastic wave equations abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 1 u in 0 with initial conditions and dirichlet boundary condition under some appropriate assumption on g by introducing a potential well we establish the global existence result for the equation above furthermore we investigate explicit exponential energy decay of the viscoelastic wave equation under the potential well

energy decay rates for von karman system with memory and boundary feedback abstract in this paper we study the von karman plate model with long range memory and boundary nonlinear feedback we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

asymptotic behavior of solutions of the one dimensional wave equation with a nonlinear boundary stabilizer the modeling of nonlinear passive damping devices or boundary frictions of an otherwise linear vibrating system often results in nonlinear elastic dissipative boundary conditions such systems occur increasingly often in engineering applications whose control and stability analysis appear much more complex than the classical linear distributed parameter systems this paper uses the method of characteristics and nonlinear semigroup theory to study the effect of nonlinear boundary stabilization and analyze the asymptotic behavior of solutions of such systems the authors are able to determine the omega limit set of the dynamical system and the asymptotic rates of various solutions to the omega limit set

smoothing effect and propagations of singularities for viscoelastic plates abstract we study dissipative models for plates and we show that the solutions have a smoothing effect on the initial data for viscous plates while for materials with memory the solution propagates singularities that is the solution of the plate equation of memory type is as regular as the initial data moreover we show that when both dissipations are present the memory type prevails in the sense that the solution propagates singularities finally we prove the existence of global solutions for non linear dissipative equations with small data which decay exponentially as time goes to infinity

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

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

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

asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel in this paper we consider a problem which arises in viscoelasticity we prove an exponential decay of solutions under weaker assumptions than the ones frequently used in the literature in particular the kernels we are considering are not necessarily exponentially decaying to zero as was assumed before the present results improve also a previous work of the authors

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

efficient gaussian process regression for large datasets gaussian processes are widely used in nonparametric regression classification and spatiotemporal modelling facilitated in part by a rich literature on their theoretical properties however one of their practical limitations is expensive computation typically on the order of n3 where n is the number of data points in performing the necessary matrix inversions for large datasets storage and processing also lead to computational bottlenecks and numerical stability of the estimates and predicted values degrades with increasing n various methods have been proposed to address these problems including predictive processes in spatial data analysis and the subset of regressors technique in machine learning the idea underlying these approaches is to use a subset of the data but this raises questions concerning sensitivity to the choice of subset and limitations in estimating fine scale structure in regions that are not well covered by the subset motivated by the literature on compressive sensing we propose an alternative approach that involves linear projection of all the data points onto a lower dimensional subspace we demonstrate the superiority of this approach from a theoretical perspective and through simulated and real data examples

uniform boundedness and stability for a viscoelastic problem in this paper we consider the following integro differential problem which appears in viscoelasticityu t ru t email protected du t email protected email protected du t email protected email protected t 0on a bounded domain w with dirichlet boundary condition and initial values we prove an exponential decay result under different sufficient conditions on the relaxation function than the standard ones

global nonexistence of positive initial energy solutions for a viscoelastic wave equation abstract in this paper we consider the nonlinear viscoelastic equation u t u t t u 0 t g t u d u t m 2 u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we prove the nonexistence of global solutions with positive initial energy

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

general decay rate estimate for a viscoelastic equation with weakly nonlinear time dependent dissipation and source terms a viscoelastic wave equation in canonical form with weakly nonlinear time dependent dissipation and source terms is investigated in this paper for a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin we establish an explicit and general energy decay rate result

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

note on intrinsic decay rates for abstract wave equations with memory in this paper we consider a viscoelastic abstract wave equation with memory kernel satisfying the inequality g h g 0 s 0 where h s is a given continuous positive increasing and convex function such that h 0 0 we shall develop an intrinsic method based on the main idea introduced by lasiecka and tataru uniform boundary stabilization of semilinear wave equation with nonlinear boundary dissipation differential and integral equations 6 507 533 1993 for determining decay rates of the energy given in terms of the function h s this will be accomplished by expressing the decay rates as a solution to a given nonlinear dissipative ode we shall show that the obtained result while generalizing previous results obtained in the literature is also capable of proving optimal decay rates for polynomially decaying memory kernels h s sp and for the full range of admissible parameters p 1 2 while such result has been known for certain restrictive ranges of the parameters p 1 3 2

the thermoelastic and viscoelastic contact of two rods we consider the thermoelastic and viscoelastic contact problem of two rods and prove the existence of a weak solution using a penalization method and compensated compactness moreover for the thermoelastic contact we show that the weak solution converges to zero exponentially as time goes to infinity and for the viscoelastic contact we prove that the weak solution decays to zero with the same rates as the relaxation functions do

exponential and polynomial decay for a quasilinear viscoelastic equation abstract we consider the following nonlinear viscoelastic equation u t u t t u u t t 0 t g t s u s d s 0 in a bounded domain for 0 we show that the dissipation induced by the integral term is strong enough to stabilize the solution this result improves an earlier one given by cavalcanti et al in m m cavalcanti v n d cavalcanti j ferreira existence and uniform decay for nonlinear viscoelastic equation with strong damping math methods appl sci 24 2001 1043 1053

general decay and blow up of solutions for a system of viscoelastic wave equations with nonlinear boundary source terms abstract in this work an initial boundary value problem for a system of viscoelastic wave equations with nonlinear boundary source term of the form u i t t u i u i t t 0 t g i t s u i s d s u i t 0 in 0 t u i x 0 i x u i t x 0 i x in u i x t 0 on 0 0 t u i t t u i 0 t g i t s u i s d s u i t f i u 0 on 1 0 t where i 1 l l 2 is considered in a bounded domain in r n n 1 by the faedo galerkin approximation method we obtain existence and uniqueness of weak solutions under appropriate assumptions on initial data and the relaxation functions we establish general decay and blow up results associated to solution energy estimates for lifespan of solutions are also given

blow up in a nonlinear viscoelastic wave equation with strong damping abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy

some well posedness and general stability results in timoshenko systems with infinite memory and distributed time delay in this paper we consider a timoshenko system in one dimensional bounded domain with infinite memory and distributed time delay both acting on the equation of the rotation angle without any restriction on the speeds of wave propagation and under appropriate assumptions on the infinite memory and distributed time delay convolution kernels we prove first the well posedness and second the stability of the system where we present some decay estimates depending on the equal speed propagation case and the opposite one the obtained decay rates depend on the growths of the memory and delay kernels at infinity in the nonequal speed case the decay rate depends also on the regularity of initial data our stability results show that the only dissipation resulting from the infinite memory guarantees the asymptotic stability of the system regardless to the speeds of wave propagation and in spite of the presence of a distributed time delay applications of our approach to specific coupled timoshenko heat and timoshenko wave systems as well as the discrete time delay case are also presented

on the exponential decay of waves with memory in this paper we consider general linear damped wave equations with memory we establish energy estimates that under the assumption of exponentially bounded kernels induce exponential decaying solutions numerical waves that mimic their continuous counterpart are also introduced using a finite element approach

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

global existence and uniform decay for a nonlinear viscoelastic equation with damping abstract in this paper we investigate a nonlinear viscoelastic equation with linear damping global existence of weak solutions and the uniform decay estimates for the energy have been established

a dimension reduced approach to space time kalman filtering summary many physical biological processes involve variability over both space and time as a result of difficulties caused by large datasets and the modelling of space time and spatiotemporal interactions traditional space time methods are limited in this paper we present an approach to space time prediction that achieves dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive that is it exploits the unidirectional flow of time in an autoregressive framework and is spatially descriptive in that the autoregressive process is spatially coloured with the inclusion of a measurement equation this formulation naturally leads to the development of a spatio temporal kalman filter that achieves dimension reduction in the analysis of large spatio temporal datasets unlike other recent space time kalman filters our model also allows a nondynamic spatial component the method is applied to a dataset of near surface winds over the topical pacific ocean spatial predictions with this dataset are improved by considering the additional non dynamic spatial process the improvement becomes more pronounced as the signal to noise ratio decreases

general decay and blow up of solution for a quasilinear viscoelastic problem with nonlinear source abstract in this paper we consider a quasilinear viscoelastic wave equation in canonical form with the homogeneous dirichlet boundary condition we prove that for certain class of relaxation functions and certain initial data in the stable set the decay rate of the solution energy is similar to that of the relaxation function this result improves earlier ones obtained by messaoudi and tatar s a messaoudi n e tatar global existence and uniform stability of solutions for a quasilinear viscoelastic problem math methods appl sci 30 2007 665 680 in which only the exponential and polynomial decay rates are considered conversely for certain initial data in the unstable set there are solutions that blow up in finite time the last result is new since it allows a larger class of initial energy which may take positive values