the lack of polynomial stability to mixtures with frictional dissipation abstract we consider the system modeling a mixture of n materials with frictional damping we show that the corresponding semigroup is exponentially stable if and only if the imaginary axis is contained in the resolvent set of the infinitesimal generator in particular this implies the lack of polynomial stability to the corresponding semigroup

indirect stabilization of a mindlin timoshenko plate abstract in this note we investigate stability issues for a mindlin timoshenko plate with internal dissipation distributed everywhere in the domain under consideration the damping occurs only in the elasticity equations describing the motion of the angles of rotation of a filament the vertical deflection equation has no damping but the effect of the damping is transmitted there by the coupling a natural question is then is the coupling robust enough to induce the exponential stability of the mindlin timoshenko plate a positive response to that question is given in this note provided that the plate is clamped dirichlet boundary conditions and the speed of propagation of the wave generated by the longitudinal component of the rotation angles and that of the wave generated by the vertical deflection are identical this result strongly improves earlier results where only polynomial stability was established when those speeds are distinct an improved polynomial stability of the system is established the proofs of those stability results are constructive and they rely on the frequency domain method combined with the multipliers technique in particular the exponential stability result seems to be the first one for the mindlin timoshenko system where the mechanical damping is present in the rotation angle equations only

stability radius and internal versus external stability in banach spaces an evolution semigroup approach in this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems these include autonomous and nonautonomous systems modeled with unbounded state space operators acting on banach spaces this approach allows one to apply the classical theory of strongly continuous semigroups to time varying systems in particular the complex stability radius may be expressed explicitly in terms of the generator of an evolution semigroup examples are given to show that classical formulas for the stability radius of an autonomous hilbert space system fail in more general settings upper and lower bounds on the stability radius are proven for banach space systems in addition it is shown that the theory of evolution semigroups allows for a straightforward operator theoretic analysis of internal stability as determined by classical frequency domain and input output operators even for nonautonomous banach space systems in particular for the nonautonomous setting internal stability is shown to be equivalent to input output stability for stabilizable and detectable systems for the autonomous setting an explicit formula for the norm of input output operator is given

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

the hartman grobman theorem for semilinear hyperbolic evolution equations abstract the famous hartman grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in banach spaces by means of simple direct proof it is also shown that the linearising map is holder continuous several applications to abstract and specific damped wave equations are given to demonstrate the strength of our results

decay rates for the three dimensional linear system of thermoelasticity we consider the two and three dimensional system of linear thermoelasticity in a bounded smooth domain with dirichlet boundary conditions we analyze whether the energy of solutions decays exponentially uniformly to zero as t to infty first of all by a decoupling method we reduce the problem to an observability inequality for the lame system in linear elasticity and more precisely to whether the total energy of the solutions can be estimated in terms of the energy concentrated on its longitudinal component we show that when the domain is convex the decay rate is never uniform in fact the lack of uniform decay holds in a more general class of domains in which there exist rays of geometric optics of arbitrarily large length that are always reflected perpendicularly or almost tangentially on the boundary we also show that in three space dimensions the lack of uniform decay may also be due to a critical polarization of the energy on the transversal component of the displacement in two space dimensions we prove a sufficient and almost necessary condition for the uniform decay to hold in terms of the propagation of the transversal characteristic rays under the further assumption that the boundary of the domain does not have contacts of infinite order with its tangents we also give an example due to d hulin in which these geometric properties hold in three space dimensions we indicate without proof how a careful analysis of the polarization of singularities may lead to sharp sufficient conditions for the uniform decay to hold in two space dimensions we prove that smooth solutions decay polynomially in the energy space to a finite dimensional subspace of solutions except when the domain is a ball or an annulus finally we discuss some closely related controllability and spectral issues

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

bases for parametrized iterativity parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables chosen as a parameter we show how such algebras can be introduced in an arbitrary category a by employing a base i e an operation interpreting objects of a as monads on a for every base we prove that free base algebras and free iterative base algebras exist the main result is a coalgebraic construction of the latter all equation morphisms form a diagram whose colimit is proved to be a free iterative base algebra

duality theory for maximizations with respect to cones generalizations of pareto optimality have been studied by a number of authors in finite dimensions such work is exemplified by corley s 1 dacunha and polak lo goeffrion 131 hartley 151 lin 171 tanino and sawaragi 1211 wendell and lee 22 and yu 23 the optimization of functions into possibly infinite dimensions has been considered by borwein 121 cesari and suryanarayana 3 christopeit 4 corley 6 7 craven s 91 hurwicz 16 1 neustadt 19 1 and ritter 20 an extensive bibliography on pareto optimality its extensions and applications is given in 111 in this paper a duality theory is developed using the concept of saddlepoints for a problem in which the maximization of a function into possibly infinite dimensions is defined in terms of a cone the results here extend the work of tanino and sawaragi 21 to infinite dimensions a distinction is also made here between the notions of weak and strong optimality distinguishing between the two concepts allows the removal of the assumption of properness in 211 in establishing a relationship between the primal and dual problems as well as permits additional duality relationships to be proved

the lack of exponential stability in certain transmission problems with localized kelvin voigt dissipation in this paper we consider the transmission problem of a material composed of three components one of them is a kelvin voigt viscoelastic material the second is an elastic material no dissipation and the third is an elastic material inserted with a frictional damping mechanism the main result of this paper is that the rate of decay will depend on the position of each component when the viscoelastic component is not in the middle of the material then there exists exponential stability of the solution instead when the viscoelastic part is in the middle of the material there is not exponential stability in this case we show that the corresponding solution decays polynomially as 1 t 2 moreover we show that the rate of decay is optimal over the domain of the infinitesimal generator finally using a second order scheme that ensures the decay of energy newmark beta method we give some numerical examples which demonstrate this asymptotic behavior

the dirichlet neumann boundary control problem associated with maxwell s equations in a cylindrical region in a cylindrical region we consider electromagnetic fields independent of the axial coordinate controlling the time evolution of such fields by means of boundary currents likewise independent of the axial direction is equivalent to controlling simultaneously two wave equations one with boundary control of dirichlet type the other of neumann type in this paper we provide a preliminary study of control problems of this type and indicate what is necessary for extensions of our work

on efficiency and duality for multiobjective programs abstract for a multiobjective nonlinear program which involved inequality and equality constraints wolfe mond weir and general mond weir type duals are formulated and the concept of efficiency pareto optimum is used to state some duality results under generalized f convexity assumptions

decay rates for 1 d mixed type ii and type iii thermoelastic system with localized viscous damping abstract this work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1 d elastic systems the spatial domain of the 1 d thermoelastic system under consideration can be divided into three sub intervals that is the thermoelastic region of type ii the one of type ii with viscous damping and the one of type iii the following two kinds of energy decay rates for the system are obtained 1 if the thermoelastic region of type iii includes one exterior point of the spatial domain of the system the energy of the system decays exponentially 2 if not that is the thermoelastic region of type iii is strictly inside the spatial domain the system always lacks of exponential decay however the optimal polynomial decay rate is further estimated for this system with smooth initial states finally some numerical simulations are presented to verify the stability results obtained in this work

conditional stability of unstable viscous shock waves in compressible gas dynamics and mhd extending our previous work in the strictly parabolic case we show that a linearly unstable lax type viscous shock solution of a general quasilinear hyperbolic parabolic system of conservation laws possesses a translation invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small l 1 h 3 perturbations converging time asymptotically to a translate of the unperturbed wave that is for a shock with p unstable eigenvalues we establish conditional stability on a codimension p manifold of initial data with sharp rates of decay in all l p for p 0 we recover the result of unconditional stability obtained by mascia and zumbrun the main new difficulty in the hyperbolic parabolic case is to construct an invariant manifold in the absence of parabolic smoothing

vector maximisation and lagrange multipliers the lagrangean function for scalar constrained optimisation problems is extended in a directly analogous manner to constrained vector optimisation problems some simple saddle point results are presented for vector maxima sets conditions are given for the characterisation of the vector maximum set of the original vector problem in terms of the vector maximum sets with respect to the vector lagrangeans

on uniform decay of a nonsimple thermoelastic bar with memory abstract in this paper we investigate the asymptotic behavior of a one dimensional problem of linear theory of nonsimple thermoelasticity with hereditary heat conduction we show that the corresponding semigroup is exponentially stable when the thermal memory kernel decays exponentially for large time but not analytic we conclude by showing the impossibility of localization in time of the solutions

stability of post fertilization traveling waves article history this paper studies the stability of a family of traveling wave solutions to the system proposed by lane et al d c lane j d murray v s manoranjan analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post fertilization waves on eggs ima j math appl med biol 4 4 1987 309 331 to model a pair of mechanochemical phenomena known as post fertilization waves on eggs the waves consist of an elastic deformation pulse on the egg s surface and a free calcium concentration front the family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration this work establishes the spectral linear and nonlinear orbital stability of these post fertilization waves for small values of the coupling parameter the usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation nonetheless exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established we show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase modulated traveling

on the energy decay of the linear thermoelastic plate with memory abstract we analyze the longterm properties of a c 0 semigroup describing the solutions to a linear evolution system that models a thermoelastic thin plate with memory effects in the heat flux law under reasonably general assumptions on the memory kernel all single trajectories are shown to decay to zero in spite of that the semigroup is not exponentially stable

duality and saddle point type optimality for generalized nonlinear fractional programming in this paper we establish two theorems of alternative with generalized subconvexlikeness we introduce two dual models for a generalized fractional programming problem theorems of alternative are then applied to establish duality theorems and a saddle point type optimality condition

exponential stability of a mixture of two elastic solids with a degenerate weak damping mechanism abstract in this note we investigate stability issues for a mixture of two elastic solids the governing equations consist of two coupled systems of elastodynamic equations with a weak damping the damping involves the difference of velocities so that the damping operator is degenerate first we show that the underlying semigroup is strongly stable under a weaker parameters constraint thereby improving an earlier strong stability result of dafermos next we show that under extra appropriate constraints on the parameters of the coupled system the semigroup is exponentially stable our proof relies on the frequency domain method the multipliers technique and a seemingly new vector calculus identity lemma b our exponential stability result is new in the framework of mixtures involving elastodynamic equations with weak damping we also show that for some sets of parameters the system is asymptotically unstable in particular we use a concrete example to show that strong stability fails for a certain parameters constraint

vector continuous time programming without differentiability in this work continuous time programming problems of vector optimization are considered firstly a nonconvex generalized gordan s transposition theorem is obtained then the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established a scalar dual problem is introduced and duality theorems are given no differentiability assumption is imposed

mild solutions to integro differential equations in banach spaces abstract in this paper we study the existence and uniqueness of mild solutions to integro differential equations in terms of a resolvent operator on the interval 0 2 and on the real line moreover we characterize the spectrum of the resolvent family that solves the volterra equation u a u a a u f in terms of their mild periodic solutions

exponential stability in thermoviscoelastic mixtures of solids in this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one dimensional mixture of thermoviscoelastic solids our main result is to establish the exponential stability of the corresponding semigroup and the lack of exponential stability of the corresponding semigroup

spectral conditions for admissibility of evolution equations in hilbert space abstract we study properties of solutions of the evolution equation u t b u t f t where b is a closable operator on the space ap r h of almost periodic functions with values in a hilbert space h such that b commutes with translations the operator b generates a family b of closed operators on h such that b e i t x e i t b x whenever e i t x d b for a closed subset r we prove that the following properties i and ii are equivalent i for every function f ap r h such that f there exists a unique mild solution u ap r h of eq such that u ii b i is invertible for all and sup b i 1

infinite trees and completely iterative theories a coalgebraic view infinite trees form a free completely iterative theory over any given signature this fact proved by elgot bloom and tindell turns out to be a special case of a much more general categorical result exhibited in the present paper we prove that whenever an endofunctor h of a category has final coalgebras for all functors h x then those coalgebras tx form a monad this monad is completely iterative i e every guarded system of recursive equations has a unique solution and it is a free completely iterative monad on h the special case of polynomial endofunctors of the category set is the above mentioned theory or monad of infinite trees this procedure can be generalized to monoidal categories satisfying a mild side condition if for an object h the endofunctor h i has a final coalgebra t then t is a monoid this specializes to the above case for the monoidal category of all endofunctors

stability of bright solitary wave solutions to perturbed nonlinear schrodinger equations abstract the propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear schrodinger equation nls when considering realistic fibers one must examine perturbed nls equations with the particular perturbation depending on the physical situation that is being modeled a common example is the complex ginzburg landau equation cgl which is a dissipative perturbation it is known that some of the stable bright solitons of the nls survive a dissipative perturbation such as the cgl given that a wave persists it is then important to determine its stability with respect to the perturbed nls a major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum since the essential spectrum of the nls is located on the imaginary axis such eigenvalues may lead to an unstable wave in fact eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum here we present a technique which can be used to track these bifurcating eigenvalues as a consequence we are able to locate the spectrum for bright solitary wave solutions to various perturbed nonlinear schrodinger equations and determine precise conditions on parameters for which the waves are stable in addition we show that a particular perturbation the parametrically forced nls equation supports stable multi bump solitary waves the technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

logarithmic well posed approximation of the backward heat equation in banach space abstract in this paper we apply a logarithmic approximation introduced by boussetila and rebbani in order to study an ill posed cauchy problem in banach space the proposed method induces a well posed problem whose approximation parameter yields continuous dependence on modeling throughout properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in l p r 1 p

frequency domain approach for the polynomial stability of a system of partially damped wave equations in this paper we study the stability of a system of wave equations which are weakly coupled and partially damped using a frequency domain approach based on the growth of the resolvent on the imaginary axis we establish the polynomial energy decay rate for smooth initial data we show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations

algebras with parametrized iterativity iterative algebras as studied by nelson and tiuryn are generalized to algebras whose iterativity is parametrized in the sense that only some variables can be used for iteration for example in the case of one binary operation the free iterative algebra is the algebra of all rational binary trees if only the left hand variable is allowed to be iterated then the free iterative algebra is the algebra of all right well founded rational binary trees in order to express such parametrized iterativity we work with parametrized endofunctors of set i e finitary endofunctors h setxset set and introduce the concept of iterativity for algebras for the endofunctor email protected h x x we then describe free iterative h algebras

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

base modules for parametrized iterativity the concept of a base that is a parametrized finitary monad which we introduced earlier followed the footsteps of tarmo uustalu in his attempt to formalize parametrized recursion we proved that for every base free iterative algebras exist and we called the corresponding monad the rational monad of the base here we introduce modules for a base and we prove that the rational monad of a base gives rise to a canonical module that is characterized as the free iterative module on the given base this generalizes the classical nonparametric case of iterative s algebras whose rational monad is the monad of rational s trees and that was characterized by calvin elgot et al as the free iterative monad on s a basic parametrized example is the base assigning to every parameter set x the monad a x xa whose rational monad is the monad of all right wellfounded rational binary trees the rational module for this base is the natural transformation x xx xa x xa given by parametrized concatenation

on the rate of decay in interacting continua with memory abstract this paper is concerning the linear theory of isothermal interacting continua with memory we consider anti plane shear deformations in a mixture of two elastic solids where the dissipation mechanisms can be the viscosity in one of the components and the viscosity with respect to the relative displacement we have seen that when the only dissipation mechanism applies on the relative displacement we cannot expect the exponential decay for the solutions we have also analyzed the case when the viscosity mechanism applies on a constituent we have seen that generically the decay is of exponential type however if the coupling constitutive parameter vanishes the decay is slow

exponential decay of solutions in type ii porous thermo elasticity with quasi static microvoids abstract in this note we study the problem proposed by the one dimensional thermo porous elasticity of type ii with quasi static microvoids or in mathematical terms when the second time derivative of the volume fraction is so small that it can be negligible it is known that the isothermal deformations decay in a slow way here we prove that the introduction of a conservative mechanism as it is the type ii heat conduction makes the deformations damp generically in an exponential way which is a striking fact

evolutionary semigroups and dichotomy of linear skew product flows on locally compact spaces with banach fibers abstract we study evolutionary semigroups generated by a strongly continuous semi cocycle over a locally compact metric space acting on banach fibers this setting simultaneously covers evolutionary semigroups arising from non autonomous abstract cauchy problems and c 0 semigroups and linear skew product flows the spectral mapping theorem for these semigroups is proved the hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew product flow to this end a banach algebra of weighted composition operators is studied the results are applied in the study of roughness of the dichotomy dichotomy and solutions of nonhomogeneous equations green s function for a linear skew product flow pointwise dichotomy versus global dichotomy and evolutionary semigroups along trajectories of the flow

asymptotic stability of semigroups associated with linear weak dissipative systems with memory we study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations we show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution in the case of the lack of exponential decay we find the polynomial rate of decay of the solution some examples are given

robustness with respect to delays for exponential stability of distributed parameter systems in this paper we address the question of whether the open loop exponential growth rate of a linear system can be improved by a feedback in such a way that this improvement is robust with respect to small delays in the feedback loop when the input operator is admissible and the class of possible feedbacks consists of compact operators we find that if a feedback can improve the exponential growth rate then it can do so robustly furthermore we find that if the control space is finite dimensional and a bounded feedback cannot be found to improve exponential stability then a large class of unbounded feedbacks cannot improve the exponential growth rate robustly even if such feedbacks can improve the exponential growth rate in the absence of delays

a characterization of weakly efficient points in this paper we study a characterization of weakly efficient solutions of multiobjective optimization problems mops we find that under some quasiconvex conditions of the objective functions in a convex set of constraints weakly efficient solutions of an mop can be characterized as an optimal solution to a scalar constraint problem in which one of the objectives is optimized and the remaining objectives are set up as constraints this characterization is much less restrictive than those found in the literature up to now

asymptotic behavior of the energy for a class of weakly dissipative second order systems with memory a class of second order abstract systems with memory and dirichlet boundary conditions is investigated by suitable liapunov functionals existence of solutions as well as asymptotic behavior are determined in particular when the memory kernel decays exponentially the polynomially decay of the solutions is proved

duality in nondifferentiable vector programming in this paper we study the saddle point optimality conditions and lagrange duality in multiobjective optimization for generalized subconvex like functions we obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined we also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

d invexity and optimality conditions abstract in this paper a generalization of convexity called d invexity is introduced substituting d invex for convex we get some optimality conditions for nondifferentiable multiobjective programming the application is demonstrated by an example

stability of perturbed linear distributed parameter systems we present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup when this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup for generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form ha with the estimate is given in terms of the norm of the solution of the lyapunov equation which corresponds to the unperturbed system