stability of the difference type methods for linear volterra equations in hilbert spaces we study the stability of backward difference timestepping method for linear volterra equations of scalar type in a hilbert space framework the results and methods extend and simulate numerically those introduced by pruss for integrability with respect to continuous solutions

asymptotic behaviour of resolvents of abstract volterra equations abstract we give necessary and sufficient conditions for certain volterra integral and integrodifferential equations in some banach space to have a resolvent that belongs to some weighted l 1 space these conditions involve the invertibility of functions of the laplace transforms of the kernels

weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

consistent and mimetic discretizations in general relativity a discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level such discretizations have been found useful in continuum mechanics and in electromagnetism we have recently introduced a new technique for discretizing constrained theories the technique yields discretizations that are consistent in the sense that the constraints and evolution equations can be solved simultaneously but it cannot be considered mimetic since it achieves consistency by determining the lagrange multipliers in this paper we would like to show that when applied to general relativity linearized around a minkowski background the technique yields a discretization that is mimetic in the traditional sense of the word we show this using the traditional metric variables and also the ashtekar new variables but in the latter case we restrict ourselves to the euclidean case we also argue that there appear to exist conceptual difficulties to the construction of a mimetic formulation of the full einstein equations and suggest that the new discretization scheme can provide an alternative that is nevertheless close in spirit to the traditional mimetic formulations

classification of constraints and degrees of freedom for quadratic discrete actions we provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions this classification is based on the different types of null vectors of the lagrangian two form and employs the canonical formalism developed in dittrich and hohn constraint analysis for variational discrete systems j math phys 54 093505 2013 e print arxiv 1303 4294 math ph and hohn quantization of systems with temporally varying discretization i evolving hilbert spaces j math phys 55 083508 2014 e print arxiv 1401 6062 gr qc the analysis is carried out in both the classical and quantum theory and applies to systems with both temporally varying or constant discretization in particular it is shown explicitly how changes in the discretization e g resulting from canonical coarse graining or refining operations or an evolving background geometry change the dynamical content of the system it is demonstrated how on a temporally varyi

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

quantization of systems with temporally varying discretization ii local evolution moves several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves local evolution moves in variational discrete systems 1 are a generalization of the pachner evolution moves of simplicial gravity models 2 update only a small subset of the dynamical data 3 change the number of kinematical and physical degrees of freedom and 4 generate a dynamical or canonical coarse graining or refining of the underlying discretization to systematically explore such local moves and their implications in the quantum theory this article suitably expands the quantum formalism for global evolution moves constructed in paper i p a hohn quantization of systems with temporally varying discretization i evolving hilbert spaces j math phys 55 083508 2014 e print arxiv 1401 6062 gr qc by employing that global moves can be decomposed into sequences of local moves this formalism is spelled out for systems with euclidean configuration spaces various types of local moves the different kinds of constraints generated by them the constraint preservation and possible divergences in resulting state sums are discussed it is shown that non trivial local coarse graining moves entail a non unitary projection of physical hilbert spaces and fine grained dirac observables defined on them identities for undoing a local evolution move with its time reversed inverse are derived finally the implications of these results for a pachner move generated dynamics in simplicial quantum gravity models are commented on

strong solutions to stochastic volterra equations in this paper stochastic volterra equations admitting exponentially bounded resolvents are studied after obtaining convergence of resolvents some properties for stochastic convolutions are studied our main results provide sufficient conditions for strong solutions to stochastic volterra equations

experiments and analysis on chaotic vibrations of a shallow cylindrical shell panel abstract detailed experimental results and analytical results are presented on chaotic vibrations of a shallow cylindrical shell panel subjected to gravity and periodic excitation the shallow shell panel with square boundary is simply supported for deflection in plane displacement at the boundary is elastically constrained by in plain springs in the experiment the cylindrical shallow shell panel with thickness 0 24 mm square form of length 140 mm and mean radius 5150 mm is used for the test specimen all edges around the shell boundary are simply supported by adhesive flexible films first to find fundamental properties of the shell panel linear natural frequencies and characteristics of restoring force of the shell panel are measured these results are compared with the relevant analytical results then geometrical parameters of the shell panel are identified exciting the shell panel with lateral periodic acceleration nonlinear frequency responses of the shell panel are obtained by sweeping the frequency of periodic acceleration in typical ranges of the exciting frequency predominant chaotic responses are generated time histories of the responses are recorded for inspection of the chaos in the analysis the donnell equation with lateral inertia force is introduced assuming mode functions the governing equation is reduced to a set of nonlinear ordinary differential equations by the galerkin procedure periodic responses are calculated by the harmonic balance method chaotic responses are integrated numerically by the runge kutta gill method the chaotic responses which are obtained by the experiment and the analysis are inspected with the fourier spectra the poincare projections the maximum lyapunov exponents and the lyapunov dimension it is found that the dominant chaotic responses of the shell panel are generated from the responses of the sub harmonic resonance of 1 2 order and of the ultra sub harmonic resonance of 2 3 order by the convergence of the maximum lyapunov exponent to the embedding dimension the number of predominant vibration modes which contribute to the chaos is found to be three or four fairly good agreements are obtained between the experimental results and the analytical results

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

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

numerical solution of parabolic integro differential equations by the discontinuous galerkin method the numerical solution of a parabolic equation with memory is considered the equation is first discretized in time by means of the discontinuous galerkin method with piecewise constant or piecewise linear approximating functions the analysis presented allows variable time steps which as will be shown call then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data the combination with finite element discretizat in space is also studied

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

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

impulsive neutral stochastic functional integro differential equations with infinite delay driven by fbm in this paper we study a class of impulsive neutral stochastic functional integro differential equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion fbm with hurst parameter h 1 2 1 in the hilbert space we prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non lipschitz conditions which include the classical lipschitz conditions as special case an example is provided to illustrate the theory some well known results are generalized and extended

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

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

well posedness and regularity for a class of linear thermo viscoelastic materials well posedness is demonstrated for an initial value problem of anisotropic linear thermo viscoelasticity with dirichlet and neumann boundary conditions the effect of the memory function on the regularity of the solutions is studied

integral equations as evolution equations abstract we study a class of time dependent linear integrodifferential equations ve with the evolution equation approach we determine the generators of a time dependent evolution equation de which is equivalent to the given integrodifferential equation under very general assumptions we prove the well posedness and continuity of ve from the stability of de the related question of convergence of a family of approximate solutions is examined as an application we include an example of hyperbolic integro partial differential equation to illustrate the theory

effectiveness and robustness with respect to time delays of boundary feedback stabilization in one dimensional viscoelasticity the damping effect of a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod is examined a characteristic equation is derived for the oscillatory modes and the solutions of this equation are studied by analytic and numerical methods as functions of the feedback gain parameter and of a parameter for feedback delay results are compared to recent studies of elastic materials where a feedback delay can cause exponential instability here this phenomenon depends significantly on the short time behavior of the viscoelastic memory kernel finally an existence result is given showing that the behavior of a weak solution corresponds in the expected way to the location of the characteristic roots

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity we will solve the following boundary value problem in linear viscoelasticity given the value of the stress on a part of the boundary of the domain find the stress in the whole body at all positive times using a state space setting we show that the stress field inside the body can be obtained from the boundary stress by a variation of parameters formula involving an analytic semigroup the relation between the regularities of the boundary stress and the stress inside the body is therefore characterized by the well known and rich regularity theory for analytic semigroups

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

continuation and maximal regularity of fractional order evolution equation abstract the cauchy problem of the homogeneous fractional order evolution equation and evolutionary integral equation have been considered in j fract calc 7 1995 89 and korean j comput appl math 9 2002 525 the existence and uniqueness of the solution have been proved and the continuation of the solution and its fractional order derivative has been proved here we study the maximal regularity continuation and some other properties of the cauchy problem of the non homogeneous fractional order evolution equation

a parallel method for the numerical solution of integro differential equation with positive memory abstract an efficient parallel numerical method is proposed for an integro differential equation with positive memory instead of solving the equation in classical time marching methods which require massive storage of solutions of previous time steps in order to advance to a next time step the fourier laplace transformation in time is applied to obtain a set of complex valued elliptic problems parameterized by points on a contour in the complex plane using the independence of an elliptic problem corresponding to one contour point is independent of those elliptic problems corresponding to other contour points all elliptic problems can be solved in parallel essentially without data communications then the time domain solution can be obtained by the fourier laplace inversion formula an error analysis and the numerical implementation of this parallel method is presented

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

characterizing the dynamic response of a thermally loaded acoustically excited plate abstract in this work the dynamic response is considered of a homogeneous fully clamped rectangular plate subject to spatially uniform thermal loads and narrow band acoustic excitation in both the pre and post buckled regimes the small amplitude linear response is confirmed however the primary focus is on the large amplitude non linear snap through response because of the obvious implications for fatigue in aircraft components a theoretical model is developed which uses nine spatial modes and incorporates initial imperfections and non ideal boundary conditions because of the higher order nature of this model it is inherently more complicated than a one mode buckled beam equation duffing s equation an experimental system was developed to complement the theoretical results and also to measure certain system parameters for the model which are not available theoretically several analysis techniques are used to characterize the response these include time series power spectra and autocorrelation functions in addition the fractal dimension and lyapunov exponents for the response are computed to address the issue of spatial dimension and temporal complexity chaos respectively comparisons between theory and experiment are made and show considerable agreement however these comparisons also serve to point out difficulties in computing the fractal dimension and lyapunov exponents from experimental data

existence and regularity for a class of integrodifferential equations of parabolic type the method we use rests on the inversion of the formal laplace transform of r and allows one to analyze the regularity of the solution u problem 1 1 has been studied by several authors using various methods see for instance l 18 211 the laplace transform approach presented here has been used in s 7 9 14 153 in our previous papers s 7 93 we have in fact analyzed a more general situation while here we take full 36 0022 247x 85 3 00

existence results for impulsive neutral stochastic functional integro differential inclusions with nonlocal initial conditions in this paper we prove the existence of mild solutions for a class of impulsive neutral stochastic functional integro differential inclusions with nonlocal initial conditions and resolvent operators sufficient conditions for the existence are derived with the help of the fixed point theorem for multi valued operators due to dhage and the fractional power of operators an example is provided to illustrate the theory

modal interaction in chaotic vibrations of a shallow double curved shell panel abstract experimental results and analytical results are presented on chaotic vibrations of a shallow double curved shell panel subjected to gravity and periodic excitation modal interactions in the chaotic responses are discussed the shell panel with square boundary is simply supported for deflection in plane displacement at the boundary is elastically constrained in the experiment time histories of the chaotic responses at the spatial multiple positions of the shell panel are measured for the inspection of modal interaction in the analysis the shallow shell panel is assumed to have constant curvatures along to orthogonal directions and geometric initial imperfection the donnell mushtari vlasov type equation is used as governing equation with lateral inertia force assuming deflection with multiple modes of vibration the governing equation is reduced to a set of nonlinear ordinary differential equations by the bubnov galerkin procedure chaotic responses are integrated numerically the chaotic responses which are obtained by the experiment and the analysis are inspected with the fourier spectra the poincare projections the maximum lyapunov exponents and the lyapunov dimension contribution of modes of vibration to the chaotic responses is analyzed by the principal component analysis i e karhunen loeve transformation

obituary to a j pritchard on the 12th of august 2007 tony pritchard professor of mathematics at the university of warwick died suddenly at the age of 70 from a heart attack while on holiday with his family on the island of lanzarote both of the authors have had the privilege of working with him for many years we have lost both a colleague and a friend the following notes are dedicated to his memory

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

dirac type approach for consistent discretizations of classical constrained theories we analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time we prove that under very general conditions it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the poisson or dirac bracket structure the conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated lagrange multipliers the gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations the resulting scheme is general enough to accommodate the treatment of field theories on the lattice this paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems including yang mills theories bf theory and gen

weighted l1 paley wiener theorem with applications to stability of the linear multi step methods for volterra equations in hilbert spaces abstract we study the weighted l 1 paley wiener theorem with applications to stability of the linear multi step time discretization for a linear volterra equation of scalar type in a hilbert space the results extend to weighted l 1 stability some recent l 1 stability theorem due to the author numer math 109 2008 571 595 our theoretical results are applied to investigate the asymptotic behavior as t n of the numerical solutions of certain integro differential equations in hilbert space

fractional order evolutionary integral equations the topic of fractional calculus derivatives and integrals of arbitrary orders is enjoying growing interest not only among mathematicians but also among physicists and engineers also the evolutionary integral equations have many applications in applied mathematics in this work we are concerned with a class of evolutionary integral equations of arbitrary fractional orders the existence uniqueness and some other properties of the solutions will be proved also the continuation of the problems will be established

quantization of systems with temporally varying discretization i evolving hilbert spaces a temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics to better understand such discretization changing dynamics in the quantum theory an according formalism for constrained variational discrete systems is constructed while this paper focuses on global evolution moves and for simplicity restricts to flat configuration spaces rn a paper ii p a hohn quantization of systems with temporally varying discretization ii local evolution moves j math phys e print arxiv 1401 7731 gr qc discusses local evolution moves in order to link the covariant and canonical picture the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors this projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums non trivial

maximal regularity for evolution equations by interpolation and extrapolation on considere le probleme aux valeurs initiales pour l equation d evolution abstraite u t b t u t f t 0 t t ou b t est pour tout t le generateur infinitesimal d un semi groupe analytique dans un b espace e on considere le cas ou le domaine d b t de b t ne depend pas de t

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

on monotone solutions of an integrodifferential equation in linear viscoelasticity we consider the integrodifferential equation u t x int 0 t a t s u xx s x ds with initial and boundary conditions corresponding to the rayleigh problem the kernel has the form a t a 0 a infty t int 0 t a 1 s ds where a 0 geq 0 a infty geq 0 and a 1 in l loc 1 bf r is of positive type and satisfies the condition int 0 infty e epsilon t ert a 1 t ert dt 0 by solving the equation numerically and performing a careful error analysis we show that the solution u t x need not be nondecreasing in t geq 0 for fixed x 0 if a 1 is nonnegative nonincreasing and convex the same result is shown to hold under the assumption that a 1 is completely positive this answers a question that remained unsolved in j pru ss it math ann 279 1987 p 330 in the case where a 1 is convex piecewise linear the solution is shown to be almost everywhere equal to a function which is discontinuous across infinitely many parallel lines

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

constraint analysis for variational discrete systems a canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised the formalism is equivalent to the covariant formulation encompasses global and local discrete time evolution moves and naturally incorporates both constant and evolving phase spaces the latter of which is necessary for a time varying discretization the different roles of constraints in the discrete and the conditions under which they are first or second class and or symmetry generators are clarified the non preservation of constraints and the symplectic structure is discussed on evolving phase spaces the number of constraints at a fixed time step depends on the initial and final time step of evolution moreover the definition of observables and a reduced phase space is provided again on evolving phase spaces the notion of an observable as a propagating degree of freedom requires specification of an initial and final step and crucially depends on this choice in contrast to the continuum however upon restriction to translation invariant systems one regains the usual time step independence of canonical concepts this analysis applies e g to discrete mechanics lattice field theory quantum gravity models and numerical analysis

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

on linear volterra equations of parabolic type in banach spaces linear integrodifferential equations of volterra type in a banach space are studied in case the main part of the equation generates an analytic co semigroup under very general assumptions it is shown that a resolvent operator exists and that many of the solution properties of parabolic evolu tion equations are inherited the results are then applied to integro partial differential equations of parabolic type

singular relaxation moduli and smoothing in three dimensional viscoelasticity we develop a semigroup setting for linear viscoelasticity in threedimensional space with tensor valued relaxation modulus and give a criterion on the relaxation kernel for differentiability and analyticity of the solutions the method is also extended to a simple problem in thermoviscoelasticity

sensitivity to infinitesimal delays in neutral equations the stability of a steady state solution of a neutral functional differential equation can be sensitive to infinitesimal changes in the delays this phenomenon is caused by the behavior of the essential spectrum and is determined by the roots of an exponential polynomial avellar and hale j math anal appl 73 1980 pp 434 452 have considered the case of multiple fixed and nonzero delays in the first part of this paper their results are illustrated by means of spectral plots in the second part we extend the theory of avellar and hale to the limit case whereby some of the delays are brought to zero which may lead to characteristic roots with arbitrarily large real part necessary and sufficient conditions are provided using these results we show that the ratio of the delays plays a crucial role when several delays tend to zero simultaneously as an illustration of the theory we analyze the robustness of a boundary controlled pde in the presence of a small feedback delay

finite element approximation of a parabolic integro differential equation with a weakly singular kernel we give error estimates for the numerical solution by means of the galerkin finite element method of an integro differential equation of parabolic type with a memory term containing a weakly singular kernel optimal order estimates are shown for spatially semidiscrete and completely discrete methods special attention is paid to the regularity of the exact solution

approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory and an approximating technique abstract our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory the approximating technique semigroup theory and the theory of fixed point we also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system we prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be lipschitz continuous in the first case and continuous only in the second case finally the main results are illustrated using examples

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory