existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

approximate controllability for linearized compressible barotropic navier stokes system in one and two dimensions abstract in this paper we consider compressible barotropic navier stokes equations in one and two dimensions linearized around a constant steady state with dirichlet boundary conditions we explore the controllability of this linearized system using a control only for the velocity equation we prove that the system with homogeneous dirichlet boundary conditions is approximately controllable by a localized interior control when time is sufficiently large

approximate controllability of the fitzhugh nagumo equation in one dimension abstract the fitzhugh nagumo fhn equation is a simplified model of a nerve axon we explore the controllability of this model using a localized interior control only for the first equation the linearized system is not null controllable using a localized interior control since the spectrum of the linearized system has an accumulation point though it is approximate controllable we show that the solution of the fhn equation fails to be globally approximate controllable in a given time but it is possible to move from any steady state to any other steady state arbitrarily close after some appropriate time by a localized interior control provided that both steady states are in the same connected component of the set of steady states finally we make some additional remarks and comments and we mention some open questions for our system for the sake of completeness we give the details of the existence uniqueness and uniform bound of the solution in appendix

consensus of multi agent systems based on sampled data control this article studies the consensus problem in directed networks assuming that each agent is with double integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants we propose a protocol based on sampled data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol in virtue of this equivalent characterisation we further consider two cases fixed topology and switching topology for the first case we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem for the second case we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals respectively finally simulations are provided to illustrate the effectiveness of the theoretical results

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

some controllability results for linear viscoelastic fluids we analyze the controllability properties of systems which provide a description at first approximation of a kind of viscoelastic fluid we consider linear maxwell fluids first we establish the large time approximate finite dimensional controllability of the system with distributed or boundary controls supported by arbitrary small sets then we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets the proofs of these results rely on classical arguments in particular the approximate controllability result is implied by appropriate unique continuation properties while exact controllability is a consequence of observability inverse inequalities we also discuss questions concerning the controllability of viscoelastic fluids and some related open problems

consensus of heterogeneous multi agent systems without velocity measurements this article considers the consensus problem of heterogeneous multi agent system composed of first order and second order agents in which the second order integrator agents cannot obtain the velocity second state measurements for feedback two different consensus protocols are proposed first we propose a consensus protocol and discuss the consensus problem of heterogeneous multi agent system by applying the graph theory and the lyapunov direct method some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader following networks second due to actuator saturation we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi agent system finally some examples are presented to illustrate the effectiveness of the obtained criterions

integral type approximate controllability of linear parabolic integro differential equations abstract this paper addresses the study of the integral type approximate controllability of linear parabolic integro differential equations this new controllability is defined by imposing some additional integral type constraints on the usual approximate controllability and therefore can be used to keep the state close to the target the paper is concerned with a special choice of integral kernels which are multiples of the same exponential function we reduce the problem of new controllability to the obtention of a unique continuation property for the suitable adjoint system

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

group consensus control for heterogeneous multi agent systems with fixed and switching topologies abstractin this paper the group consensus problems of heterogeneous multi agent systems with fixed and switching topologies are investigated first a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi agent systems by using the neighbours information then some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus rigorous proofs are given by using graph theory matrix theory and lyapunov theory finally numerical simulations are also given to verify the theoretical analysis

nonlocal transformations of kolmogorov equations into the backward heat equation we extend and solve the classical kolmogorov problem of finding general classes of kolmogorov equations that can be transformed to the backward heat equation these new classes include kolmogorov equations with time independent and time dependent coefficients our main idea is to include nonlocal transformations we describe a step by step algorithm for determining such transformations we also show how all previously known results arise as particular cases in this wider framework

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

new classes of schrodinger equations equivalent to the free particle equation through non local transformations we introduce new classes of schrodinger equations with time dependent potentials which are transformable to the free particle equation through non local transformations these non local transformations arise when considering the potential systems of the schrodinger equation explicit formulae are given for the potentials and the corresponding solutions related to the solutions of the free particle equation

approximate controllability results for viscoelastic flows with infinitely many relaxation modes abstract we prove results on approximate controllability for linear viscoelastic flows with a localized distributed control in the momentum balance equation the constitutive law is a multimode maxwell or jeffreys model with an infinite number of relaxation modes

on the control of viscoelastic jeffreys fluids abstract this paper is devoted to analyzing the control of vicoelastic fluids of the jeffreys kind also known as oldroyd models we will present the interesting problems with special emphasis in the difficulties that they involve then we will consider appropriate linear approximations and we will establish some partial approximate finite dimensional controllability results in an arbitrarily small time with distributed or boundary controls supported by arbitrarily small sets the proofs rely on some specific unique continuation properties which are implied by the structure of the solutions

well posedness for the fene dumbbell model of polymeric flows we prove local and global well posedness for the fene dumbbell model for a very general class of potentials indeed in prior local or global well posedness results conditions on the strength of the singularity or on the parameter b were made here we give a proof in the general case we also prove global existence results if the data is small or if we restrict to the co rotational model in dimension 2 2008 wiley periodicals inc

some controllability results for the n dimensional navier stokes and boussinesq systems with n 1 scalar controls in this paper we deal with some controllability problems for systems of the navier stokes and boussinesq kind with distributed controls supported in small sets our main aim is to control n dimensional systems n 1 scalar unknowns in the case of the navier stokes equations with n 1 scalar control functions in a first step we present some global carleman estimates for suitable adjoint problems of linearized navier stokes and boussinesq systems in this way we obtain null controllability properties for these systems then we deduce results concerning the local exact controllability to the trajectories we also present global null controllability results for some truncated approximations of the navier stokes equations

sequences of related linear pdes abstract we introduce a transformation theory to generate chains of linear pdes and related solution sequences our procedure depends on representing a given linear pde in terms of a special equivalent system of two coupled linear pdes where the auxiliary dependent variable satisfies the next pde of a sequence the solution of a pde with variable coefficient depending on n 1 constants 1 2 n 1 is obtained from any solution of a pde of the same type with variable coefficient depending on n constants 1 2 n by a simple backlund transformation each sequence contains two inclusive chains since the pde with n constants is a special case of the pde with n 2 constants we generate solutions of wave equations with wave speeds c x 1 2 n fokker planck equations with drifts f x 1 2 n and diffusion equations with diffusivities k x 1 2 n where 1 2 n are arbitrary constants n 1 2 new explicit general solutions are obtained for a class of wave equations with wave speeds depending on three parameters

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

distributed consensus of heterogeneous multi agent systems with fixed and switching topologies in this article we study distributed consensus of heterogeneous multi agent systems with fixed and switching topologies the analysis is based on graph theory and nonnegative matrix theory we propose two kinds of consensus protocols based on the consensus protocol of first order and second order multi agent systems some necessary and sufficient conditions that the heterogeneous multi agent system solves the consensus problems under different consensus protocols are presented with fixed topology we also give some sufficient conditions for consensus of the heterogeneous multi agent system with switching topology simulation examples are provided to demonstrate the effectiveness of the theoretical results

on form preserving transformations for the time dependent schrodinger equation in this paper we point out a close connection between the darboux transformation and the group of point transformations which preserve the form of the time dependent schrodinger equation tdse in our main result we prove that any pair of time dependent real potentials related by a darboux transformation for the tdse may be transformed by a suitable point transformation into a pair of time independent potentials related by a usual darboux transformation for the stationary schrodinger equation thus any real potential solvable via a time dependent darboux transformation can alternatively be solved by applying an appropriate form preserving point transformation of the tdse to a time independent potential the pre eminent role of the latter type of transformations in the solution of the tdse is illustrated with a family of quasi exactly solvable time dependent anharmonic potentials

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

finite time consensus for stochastic multi agent systems in this article we study the finite time consensus in probability for stochastic multi agent systems first we give the nonlinear consensus protocol for multi agent systems with gaussian white noise and define the concept of finite time consensus in probability second we prove that multi agent systems can achieve the finite time consensus in probability under five different kinds of communication topologies by using graph theory stochastic lyapunov theory and probability theory finally some simulation examples are provided to illustrate the effectiveness of the theoretical results

how symmetries yield non invertible mappings of linear partial differential equations abstract nonlocally related partial differential equation pde systems are important in the analysis of a given pde system useful nonlocally related systems can be constructed through conservation law and symmetry based methods in this paper we focus on an application of the symmetry based method to linear pde systems in particular we show how to obtain systematically non invertible mappings of linear pdes to linear pdes as examples we obtain non invertible mappings of the kolmogorov equation with variable coefficients to the backward heat equation a pde with constant coefficients as well as non invertible mappings of linear hyperbolic pdes with variable coefficients to linear hyperbolic pdes with constant coefficients

interior approximate and null controllability of the heat equation with memory in this paper we study the approximate and null controllability of the heat equation with memory we mainly consider the distributed control case with an arbitrarily small support of the control function for each positive final time t we deduce that the approximate controllability property holds and the null controllability property fails

improving consensus and synchronizability of networks of coupled systems via adding links abstract the problem of improving the consensus and synchronizability for weighted networks of dynamic systems via adding links among them is investigated in this paper a weighted network entropy is introduced to measure the homogeneity of the weighted networks the relationship between the homogeneity and the consensus and synchronizability is analyzed a solution scheme is proposed to improve the consensus and synchronizability of the weighted networks through maximizing their homogeneity via adding as few links as possible weighted networks created from the barrat model are tested by using the proposed scheme and two commonly used link adding approaches are selected to compare with this scheme computer simulation results show that the proposed link adding scheme can enhance the consensus and the synchronizability of the weighted networks effectively and efficiently

consensus seeking of high order dynamic multi agent systems with fixed and switching topologies this article studies a consensus problem for a group of high order dynamic agents with fixed and switching topologies two linear consensus protocols which only depend on the agent s own information and its neighbours partial information are proposed respectively for the group with and without communication time delays for the case of fixed topology and zero communication time delay a necessary and sufficient condition for the consensus is established the parameter design of the protocol is also discussed under switching topology the consensus is investigated for two cases the case of zero communication time delay and the case of nonuniform communication time delays for each case a sufficient condition for the consensus is provided moreover for a group of double triple integrator agents with fixed topology and uniform constant time delay some necessary and sufficient conditions for the consensus are given finally numerical simulations are worked out to illustrate the effectiveness of the

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

global well posedness of viscoelastic fluids of oldroyd type in besov spaces abstract we investigate a system of equations concerning an incompressible viscoelastic fluid of the oldroyd type which describes one class of non newtonian fluid with memory making use of a regularization method in conjunction with bony s paraproduct decomposition we obtain the existence and uniqueness of a small global solution for the above system in the besov spaces b 2 s with s d 2 and which implies global well posedness for small data in h s with s d 2 since the sobolev space h s is embedded in b 2 s

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

on mapping linear partial differential equations to constant coefficient equations a constructive algorithm is developed to determine whether or not a given linear p d e can be mapped into a linear p d e with constant coefficients the algorithm is based on analyzing the infinitesimals of the lie group of transformations leaving invariant the given p d e as consequences in two dimensions necessary and sufficient conditions are given for mapping 1 a parabolic p d e into the heat equation 2 a hyperbolic p d e into the wave equation 3 an elliptic p d e into laplace s equation or the helmholtz equation the corresponding mappings are given explicitly

a mathematical model for the dynamics of clustering abstract the formation of several clusters arising from attracting forces between nonidentical entities or agents is a phenomenon observed in diverse fields think of people gathered through a mutual interest swarm behaviour of animals or clustering of oscillators in brain cells we introduce a dynamic model of mutually attracting agents for which we prove that the long term behaviour consists of agents organized into several groups or clusters we have completely characterized the cluster structure i e the number of clusters and their composition by means of a set of inequalities in the parameters of the model and have identified the intensity of the attraction as a key parameter governing the transition between different cluster structures the versatility of the model will be illustrated by discussing its relation to the kuramoto model and by describing how it applies to a system of interconnected water basins

intertwining relations of non stationary schrodinger operators general first and higher order intertwining relations between non stationary one dimensional schrodinger operators are introduced for the first order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in an r separation of variables the fokker planck and diffusion equations are briefly considered second order intertwining operators are also discussed within a general approach however due to its complicated structure only particular solutions are given in some detail

blinking model and synchronization in small world networks with a time varying coupling the paper proposes a new type of small world networks of cells with chaotic behavior this network consists of a regular lattice of cells with constant 2k nearest neighbor couplings and time dependent on off couplings between any other pair of cells in each time interval of duration such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times at each moment the coupling structure corresponds to a small world graph but the shortcuts change from time interval to time interval which is a good model for many real world dynamical networks it is to be distinguished from networks that have randomly chosen shortcuts fixed in time here we apply the connection graph stability method developed in the companion paper connection graph stability method for synchronized coupled chaotic systems see this issue to the study of global synchronization in this network with the time varying coupling structure in the case where the on off switching is fast with respect to the characteristic synchronization time of the network the synchronization thresholds are explicitly linked with the average path length of the coupling graph and with the probability p of shortcut switchings in this blinking model we prove that for the blinking model a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length short interactions between cells as in the blinking model are important in practice to cite prominent examples computers networked over the internet interact by sending packets of information and neurons in our brain interact by sending short pulses called spikes the rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much in this respect we believe that it is more efficient than a structure of fixed random connections