global existence and nonexistence of solution for cauchy problem of multidimensional double dispersion equations abstract in this paper we consider the cauchy problem of multidimensional generalized double dispersion equations u t t u u t t 2 u f u where f u a u p by potential well method we prove the existence and nonexistence of global weak solution without establishing the local existence theory and we derive some sharp conditions for global existence and lack of global existence solution

extrapolation algorithms for discrete signals with application in spectral estimation in this paper we present some new algorithms useful for extrapolation and spectral estimation of band limited sequences in one and two dimensions first we show that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least squares mnls extrapolation for example the iterative algorithms proposed in 2 and 8 10 are shown to be special cases of a one step gradient algorithm which has linear convergence convergence and other numerical properties are improved by going to a conjugate gradient algorithm for noisy observations these algorithms could be extended by considering a mean square extrapolation criterion which gives rise to a mean square extrapolation filter and also to a recursive extrapolation filter examples and application of these methods are given extension of these algorithms is made for problems where the signal is known to be periodic a new set of functions called the periodic discrete prolate spheroidal sequences p dpss analogous to dpss 21 22 are introduced and their properties are studied finally several of these algorithms are generalized to two dimensions and the relevant equations are given

initial boundary value problem of the generalized cubic double dispersion equation in this paper the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved the nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed

travelling wave solutions for a generalized double dispersion equation abstract we analyze the generalization of a double dispersion equation by means of the theory of symmetry reductions of partial differential equations we consider travelling wave reductions depending on the form of an arbitrary function we present some explicit solutions soliton solutions kinks and anti kinks

a global attractor for the elastic waveguide model in rn abstract this paper studies the longtime behavior of solutions to the elastic waveguide model in r n u t t u u t t 2 u u t u t u g x u f x it proves that when the space dimension n 5 under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity x h 2 h 1 h 2 h with 0 1 a global attractor which is connected

optimality of certain iterative and non iterative data extrapolation procedures abstract a fundamental aspect of many modern spectral analysis and image restoration procedures is the extrapolation of the measured data to achieve improved resolution iterative extrapolation poses some mathematical questions about convergence and about the optimality of the resulting limit we consider these questions and discuss briefly the optimality of certain non iterative extrapolation methods

global attractor for a nonlinear wave equation arising in elastic waveguide model abstract the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a nonlinear wave equation arising in an elastic waveguide model u t t u u t t 2 u u t g u f x it proves that when the space dimension n 5 under rather mild conditions the dynamical system associated with the above mentioned ibvp possesses a global attractor which is connected and has finite fractal and hausdorff dimension

optimal decay rate of solutions for cahn hilliard equation with inertial term in multi dimensions abstract the cauchy problem of the cahn hilliard equation with inertial term is considered based on green s function method together with energy estimates we get the global in time existence and optimal decay rate of solutions furthermore the viscous case is investigated in the last section

global existence and blow up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations this study deals with the analysis of the cauchy problem of a general class of nonlocal nonlinear equations modeling the bi directional propagation of dispersive waves in various contexts the nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable respectively the well known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here the class of nonlocal nonlinear wave equations also covers a variety of well known wave equations such as various forms of the boussinesq equation local existence of solutions of the cauchy problem with initial data in suitable sobolev spaces is proven and the conditions for global existence and finite time blow up of solutions are established

uniqueness and stability of an inverse problem for a phase field model using data from one component we study an inverse problem of determining a spatial varying coefficient in a parabolic hyperbolic phase field model with the following observation data of only one component the order parameter in a subdomain w satisfying email protected email protected email protected along a sufficiently large time interval and at a suitable time over the whole spatial domain based on a carleman estimate for the parabolic hyperbolic phase field system we prove the lipschitz stability and uniqueness for this inverse problem

diffuse interface model for rapid phase transformations in nonequilibrium systems a thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing to describe transformations within the diffuse interface we use the phase field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface governing equations of the phase field model are derived for the hyperbolic model a model with memory and a model of nonlinear evolution of transformation within the diffuse interface the consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation dissipation theorem a comparison with existing sharp interface and diffuse interface versions of the model is given

eventual regularity of the semigroup associated with the mono tubular heat exchanger equation with output feedback this paper is concerned with the regularity of the mono tubular heat exchanger equation with output feedback by approach of spectrum analysis it is shown that the semigroup generated by the closed loop operator consisting of the mono tubular heat exchanger equation and the output feedback law is eventually differentiable and eventually compact

global attractor for the generalized double dispersion equation abstract the paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t u u t t 2 u u t g u f x the main result is concerned with nonlinearities g u with supercritical growth in that case we construct a subclass g of the limit solutions and show that it has a weak global attractor especially in non supercritical case the weak topology becomes strong the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

cauchy problem of the generalized double dispersion equation abstract in this paper the existence and the uniqueness of the global solution for the cauchy problem of the generalized double dispersion equation are proved the blow up of the solution for the cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions

finite dimensional regulators for a class of regular hyperbolic pde systems abstractin this paper the output regulation problem is addressed for a class of linear hyperbolic infinite dimensional systems with spatially varying coefficients modelling a large class of convection dominated transport reaction systems in particular distributed parameter systems with bounded input and unbounded output operators are considered first we demonstrate a general conclusion about the exponential stability of the considered system by relating the stability to the solution of an associated differential equation based on the assumption that the hyperbolic system satisfies the exponential stability conditions the main manuscript contribution is the development of two novel finite dimensional regulators output and error feedback regulators such that the controlled output of the plant tracks a reference signal generated by a known signal process exosystem in order to guarantee the feasibility of the proposed regulators the solvability of the corresponding sylvester equations is discusse

longtime dynamics of the kirchhoff equations with fractional damping and supercritical nonlinearity abstract the paper investigates the global well posedness and the longtime dynamics of the kirchhoff equations with fractional damping and supercritical nonlinearity u t t m u 2 u u t f u g x with 1 2 1 the main results are focussed on the relationships among the growth exponent p of the nonlinearity f u the global well posedness and the longtime dynamics of the equations we show that i even if p is up to the supercritical range that is 1 p n 4 n 4 the well posedness and the longtime behavior of the solutions of the equation are of the characters of the parabolic equation ii when n 4 n 4 p n 4 n 4 the corresponding subclass g of the limit solutions exists and possesses a weak global attractor

output tracking control of a parallel flow heat exchange process abstract in this paper we consider an output tracking problem of a parallel flow heat exchange process with distributed and boundary inputs as the distributed inputs to the system the output feedback control is first applied under zero boundary inputs it is shown that the c 0 semigroup describing the closed loop system satisfies the spectrum determined growth condition next we apply a backstepping method to the design of the boundary inputs for output tracking our main result shows that the output of the system reaches a reference signal in finite time under both the output feedback control and the boundary control law derived by the backstepping method

two stream counter flow heat exchanger equation with time varying velocities abstract we study the two stream counter flow heat exchanger equation with time varying fluid velocities formulating it into a time varying boundary control system a representation formula of the solution is obtained

attractors for the cahn hilliard equation with memory in 2d abstract we deal with the memory relaxation of the cahn hilliard equation proposed by rotstein et al as a model for the phenomenological description of phase transition which contains as a particular case the hyperbolic version of the equation due to the absence of viscosity effects existence and uniqueness of solutions are far from being trivial in space dimension n 1 this paper is devoted to the analysis of energy solutions for the 2d model after discussing the well posedness of the problem we study its long term dynamics and we prove the existence and regularity of the global attractor provided that the relaxation parameter of the memory kernel is small enough

strong stability of the mono tubular heat exchanger equation with output feedback abstract we investigate asymptotic behavior of the c 0 semigroup t t associated with the mono tubular heat exchanger equation with output feedback by a perturbation method it is shown that t t is bounded if a constraint is satisfied by the parameters and the spatial distribution function further applying the arendt batty lyubich vu theorem a criterion is established to judge strong stability of t t

pointwise estimates of global small solutions to the generalized double dispersion equation abstract in this paper we investigate the initial value problem for the generalized double dispersion equation in r n under suitable conditions global classical solutions are proved for n 3 and n 1 respectively moreover pointwise estimates of global classical solutions are established when n 3 and n is an odd integer by fourier splitting frequency technique

existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force abstract in this paper we investigate the generalized double dispersion equation with periodic external force in r n we prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n 3 the proof is based on the spectral analysis for the solution operator and the contraction mapping theorem in addition we also discuss the time asymptotic stability of the time periodic solutions by continuous argument

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

asymptotic behavior of a nonisothermal viscous cahn hilliard equation with inertial term we consider a differential model describing nonisothermal fast phase separation processes taking place in a three dimensional bounded domain this model consists of a viscous cahn hilliard equation characterized by the presence of an inertial term tt being the order parameter which is linearly coupled with an evolution equation for the relative temperature the latter can be of hyperbolic type if the cattaneo maxwell heat conduction law is assumed the state variables and the chemical potential are subject to the homogeneous neumann boundary conditions we first provide conditions which ensure the well posedness of the initial and boundary value problem then we prove that the corresponding dynamical system is dissipative and possesses a global attractor moreover assuming that the nonlinear potential is real analytic we establish that each trajectory converges to a single steady state by using a suitable version of the eojasiewicz simon inequality we also obtain an estimate of the decay rate to equilibrium

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

global existence of solution for cauchy problem of multidimensional generalized double dispersion equations abstract we study the cauchy problem of a class of multidimensional generalized double dispersion equations u t t u u t t 2 u k u t f u we prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data

on the stability of a linear bioprocess model with recycle loop in this note we treat a linear bioprocess model with recycle loop and analyze the spectrum of the closed loop operator in order to discuss the exponential stability it is shown that a c sub 0 semigroup generated by the closed loop operator satisfies the spectrum determined growth assumption and that the recycle loop works effectively for the process through a numerical simulation

reconstruction from partial information with applications to tomography the problem of reconstruction from projections in hilbert space is treated an axiomatic basis is considered which leads to techniques which provide improved reconstructions by incorporating prior knowledge to tailor the hilbert space to the problem at hand when applied to reconstruction of the fourier transform of a function sampled at finitely many discrete points the procedures lead to previously derived optimal estimation techniques when applied to x ray tomography the procedures lead to new reconstruction techniques which are shown to include as a special case the minimum energy reconstruction of logan and shepp duke math j 42 1975 pp 645 659

asymptotic profile of solutions to the double dispersion equation abstract in this paper we investigate the initial value problem for the double dispersion equation in r n decay estimate and asymptotic profile of solutions to the corresponding linear problem are established the asymptotic profile of solutions to the corresponding linear problem is given by the convolution of the fundamental solutions of heat and free wave equations moreover the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear problem obtained in this paper is optimal under some conditions finally global existence and optimal decay estimate of solutions to the nonlinear problem are also established

exponential stability of a mono tubular heat exchanger equation with output feedback abstract this paper is concerned with stability analysis of a mono tubular heat exchanger equation with static output feedback the mono tubular heat exchanger equation is exponentially stable when the input variable is identically zero in this paper it is shown that the c 0 semigroup generated by the closed loop operator consisting of the mono tubular heat exchanger equation and the output feedback law satisfies the spectrum determined growth assumption