monotone methods for a finite difference system of reaction diffusion equation with time delay abstract the aim of this paper is to present some monotone iterative schemes for computing the solution of a system of nonlinear difference equations which arise from a class of nonlinear reaction diffusion equations with time delays the iterative schemes lead to computational algorithms as well as existence uniqueness and upper and lower bounds of the solution an application to a diffusive logistic equation with time delay is given

stability of volterra diffusion equations with time delays this paper is concerned with asymptotic stability of a system of reaction diffusion equations which is expressed in terms of volterra integrals under homogeneous dirichlet boundary conditions the effect of diffusion and delays on the stability of the system are analyzed and sufficient conditions are given for the existence of positive solutions of the corresponding steady state problem their global attraction with respect to nonnegative solutions of the time dependent system is discussed the main tools are lyapunov functionals positive definite kernels and laplace transforms

controllability for parabolic equations with nonlinear memory this paper is concerned with the controllability of a parabolic system with nonlinear memory based on the localized estimate of the solution we prove that the system with a superlinear growth memory is not controllable furthermore two controllability results for some initial data and targets are given as well

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

on the heat diffusion starting with degeneracy abstract in this article we study the instant smoothing property of the heat diffusion that starts with degeneracy u t t x t u f t x t 0 t x r d u 0 x u 0 x where 1 we provide the existence and uniqueness result in an appropriate sobolev space setting for a fixed f the regularity improvement in sobolev regularity from u 0 to u changes continuously along in particular the larger 0 the smaller the improvement is moreover we study a regularity relation between f and u near time t 0 as varies

rank one preservers between spaces of boolean matrices in this paper we characterize i linear transformations from one space of boolean matrices to another that send pairs of distinct rank one elements to pairs of distinct rank one elements and ii surjective mappings from one space of boolean matrices to another that send rank one matrices to rank one matrices and preserve order relation in both directions both results are proved in a more general setting of tensor products of two boolean vector spaces of arbitrary dimension

fuzzy rank preserving operators abstract analogues of characterizations of rank preserving operators on field valued matrices are determined for fuzzy matrices and for matrices over related semirings for example if m is the set of mxn fuzzy matrices and min m n 1 then a linear operator on m preserves the rank of each matrix in m if and only if it preserves the rank of those matrices in m of ranks 1 and 2 other characterizations of rank preserving operators are also given

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

bijective linear maps on semimodules spanned by boolean matrices of fixed rank abstract let m m n b be the semimodule of all m n boolean matrices where b is the boolean algebra with two elements let k be a positive integer such that 2 k min m n let b m n k denote the subsemimodule of m m n b spanned by the set of all rank k matrices we show that if t is a bijective linear mapping on b m n k then there exist permutation matrices p and q such that t a paq for all a b m n k or m n and t a pa t q for all a b m n k this result follows from a more general theorem we prove concerning the structure of linear mappings on b m n k that preserve both the weight of each matrix and rank one matrices of weight k 2 here the weight of a boolean matrix is the number of its nonzero entries

on the rate of decay of solutions of functional differential equations with infinite delay on etudie la vitesse de convergence vers zero des solutions d equations differentielles fonctionnelles a retard infini

oscillation of continuous and discrete diffusive delay nicholson s blowflies models in this paper we consider the continuous and the discrete delay diffusive nicholson s blowflies models with different types of boundary conditions our aim is to give some sufficient conditions for oscillation of all positive solutions about the positive steady state we show that these conditions have essentially first order character by reducing the problem of oscillation of the boundary value problem to that of first order delay differential or difference equation

global convergence of a reaction diffusion predator prey model with stage structure and nonlocal delays in this paper a lotka volterra type reaction diffusion predator prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated in the case of a general domain sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method numerical simulations are carried out to illustrate the main results

on fully discrete galerkin approximations for partial integro differential equations of parabolic type the subject of this work is the application of fully discrete galerkin finite element methods to initial boundary value problems for linear partial integro differential equations of parabolic type we investigate numerical schemes based on the pade discretization with respect to time and associated with certain quadrature formulas to approximate the integral term a preliminary error estimate is established which contains a term related to the quadrature rule to be specified in particular we consider quadrature rules with sparse quadrature points so as to limit the storage requirements without sacrificing the order of overall convergence for the backward euler scheme the crank nicolson scheme and a third order pade type scheme the specific quadrature rules analyzed are based on the rectangular the trapezoidal and simpson s rule for all the schemes studied optimal order error estimates are obtained in the case that the solution of the problem is smooth enough since this is important for our error analysis we also discuss the regularity of the exact solutions of our equations high order regularity results with respect to both space and time are given for the solution of problems with smooth enough data 17 refs

the stability and exponential stabilization of the heat equation with memory abstract in this paper we investigate the stability of heat equation with a constant memory kernel we prove that the system does not decay for the positive kernel and is polynomially stable but not exponentially for the negative kernel in particular a more detailed description of the decay property for the negative kernel is obtained by dividing initial values into two categories moreover we show that the system can be exponentially stabilized by boundary control for any constant memory kernel

numerical blow up analysis of linearly implicit euler method for nonlinear parabolic integro differential equations abstract the linearly implicit euler method for nonlinear parabolic integro differential equations npides on bounded domains is consideblue by approximating the local effects implicitly and nonlocal effects explicitly based on nakagawa s criteria a suitable adaptive time stepping strategy is introduced by the discrete energy instead of the infinite norm with the help of lower discrete energies the finite blow up behaviors are replicated for any positive solution numerical simulations are carried out to examine the effectiveness of our blowup analysis which also motivate furthermore to prove that a global numerical solution exists for certain npides with a weakly singular kernel

on generalized inverses of boolean matrices ii abstract analogous to minimum norm g inverses and least squares g inverses for real matrices we introduce the concepts of minimum weight g inverses and least distance g inverses for boolean matrices all those boolean matrices which admit such g inverses are characterized this paper is a continuation of 2

linear operators that strongly preserve commuting pairs of boolean matrices abstract we characterize those linear operators t on the class m of square boolean matrices respectively on the set l of symmetric boolean matrices for which t x commutes with t y if and only if x commutes with y for all x y in m respectively in l

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

the arctic rank of a boolean matrix abstract among different rank functions on tropical matrices there is one known as tropical rank which is a lower bound for any other here we introduce a new concept for being opposed to tropical rank it is called arctic which gives an upper bound for other ranks our definition is based on the perimeter notion previously studied for rank one matrices we study the arithmetic behavior of the arctic rank and compare it with that of other rank functions finally we provide an algorithm computing the arctic rank we show that no algorithm is likely to find the arctic rank in polynomial time by proving that computing the perimeter of a matrix is an np hard problem

nonnegative rank preserving operators abstract analogues of characterizations of rank preserving operators on field valued matrices are determined for matrices witheentries in certain structures s contained in the nonnegative reals for example if s is the set of nonnegative members of a real unique factorization domain e g the nonnegative reals or the nonnegative integers m is the set of m n matrices with entries in s and min m n 4 then a linear operator on m preserves the rank of each matrix in m if and only if it preserves the ranks of those matrices in m of ranks 1 2 and 4 notions of rank and linearity are defined analogously to the field valued concepts other characterizations of rank preserving operators for matrices over these and other structures s are also given

holder regularity of solutions of degenerate elliptic and parabolic equations abstract we establish the alexandroff bakelman pucci estimate the harnack inequality and the holder continuity of solutions to degenerate parabolic equations of the non divergence form lu xa 11 u xx 2 x a 12 u xy a 22 u yy b 1 u x b 2 u y u t g on x 0 with bounded measurable coefficients we also establish similar regularity results in the corresponding elliptic case

column ranks and their preservers over nonnegative real matrices the column rank of an m by n matrix a over the nonnegative reals is the dimension over the nonnegative reals of the column space of a we compare the column rank with the factor rank of matrices over the nonnegative reals we also characterize the linear operators which preserve the column rank of matrices over the nonnegative reals

on markovian kinetic equations zubarev s nonequilibrium statistical operator approach abstract generalized markovian kinetic equations obtained by the zubarev method of the nonequilibrium statistical operator nso are revised in a simple example of the spin s 1 2 coupled to its surroundings it is shown that these equations are incorrect because of an inadequate markovian approximation a correct procedure of building markovian equations of motion is constructed two different although equivalent methods the davies technique and the krylov bogoliubov mitropolsky averaging method are utilized

instability in diffusive ecological models with nonlocal delay effects abstract we propose a reaction diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate two delays are incorporated into the model one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton it is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space local and bifurcation analyses are carried out it has been shown that turing type spatial patterns occur when the diffusion coefficients vary and temporal or spatial temporal patterns occur when the delay involved in the growth response changes

primes in the semigroup of boolean matrices abstract let a b c be n n matrices of zeros and ones using boolean addition and multiplication we say that a is prime if it is not a permutation matrix and if a bc implies that b or c must be a permutation matrix conditions sufficient for a matrix to be prime are provided and a characterization of primes in terms of a nation of rank is given finally an order property of primes is used to obtain a result on prime factors

regular matrices and their strong preservers over semirings an m n matrix a over a semiring s is called regular if there is an n m matrix g over s such that aga a we study the problem of characterizing those linear operators t on the matrices over a semiring such that t x is regular if and only if x is complete characterizations are obtained for many semirings including the boolean algebra the nonnegative reals the nonnegative integers and the fuzzy scalars

finite difference reaction diffusion systems with coupled boundary conditions and time delays abstract this paper is concerned with finite difference solutions of a coupled system of reaction diffusion equations with nonlinear boundary conditions and time delays the system is coupled through the reaction functions as well as the boundary conditions and the time delays may appear in both the reaction functions and the boundary functions the reaction diffusion system is discretized by the finite difference method and the investigation is devoted to the finite difference equations for both the time dependent problem and its corresponding steady state problem this investigation includes the existence and uniqueness of a finite difference solution for nonquasimonotone functions monotone convergence of the time dependent solution to a maximal or a minimal steady state solution for quasimonotone functions and local and global attractors of the time dependent system including the convergence of the time dependent solution to a unique steady state solution also discussed are some computational algorithms for numerical solutions of the steady state problem when the reaction function and the boundary function are quasimonotone all the results for the coupled reaction diffusion equations are directly applicable to systems of parabolic ordinary equations and to reaction diffusion systems without time delays

finite difference solutions of reaction diffusion equations with continuous time delays abstract this paper is an extension of the monotone iterative methods for finite difference equations with discrete time delays to a class of nonlinear finite difference system with continuous time delays the system under consideration is a finite difference approximation of a class of reaction diffusion equations with continuous time delays in the nonlinear reaction under either dirichlet or neumann robin boundary conditions various monotone iterative schemes which depend on the property of the nonlinear reaction mechanism are developed for the computation of numerical solutions it is shown by the method of upper and lower solutions that the two sequences obtained from each iterative scheme converge monotonically from above and below respectively to a unique solution of the finite difference system applications are given to two model problems known as the diffusive logistic equation and the fisher s diffusion equation in population genetics

term rank permanent and rook polynomial preservers characterizations are obtained of those linear operators on the m n matrices over an arbitrary semiring that preserve term rank we also present characterizations of permanent and rook polynomial preserving operators on matrices over certain types of semirings our results apply to many combinatorially interesting algebraic systems including nonnegative integer matrices matrices over boolean algebras and fuzzy matrices

boundary stabilization of equilibrium solutions to parabolic equations in this note a stabilizing feedback boundary controller for the equilibrium solutions to parabolic equations with dirichlet boundary control is designed the feedback controller is expressed in terms of the eigenfunctions j corresponding to unstable eigenvalues j j 1n of the linearized equation for d 1 this stabilizing procedure is applicable for n 1 only while for d 1 it is of conditional nature requiring the independence of j n on the part of the boundary where the control is applied

boolean rank preserving operators and boolean rank 1 spaces abstract we study the extent to which certain theorems on linear operators on field valued matrices carry over to linear operators on boolean matrices we obtain analogues and near analogues of several such theorems one of these leads us to consider linear spaces of m n boolean matrices whose nonzero members all have boolean rank 1 we obtain a structure theorem for such spaces that enables us to determine the maximum boolean dimension of such spaces and their maximum cardinality

spanning column ranks and their preservers of nonnegative matrices abstract this paper concerns a certain column rank of matrices over the nonnegative reals we call it the spanning column rank we have a characterization of spanning column rank 1 matrices we also investigate the linear operators which preserve the spanning column ranks of matrices over the nonnegative part of a certain unique factorization domain in the reals

primitive exponent preservers abstract let m n b denote the set of n n 0 1 matrices with boolean arithmetic the set of primitive matrices of exponent k denoted e k is the set of matrices such that a k has all nonzero entries and a j has zero entries for all j k for 3 k n we characterize those linear operators that map e k to e k and e k 1 to e k 1 we also characterize those linear operators that strongly preserve e k for 3 k n that is that map e k to e k and the complement of e k to the complement of e k

controllability and observability of a heat equation with hyperbolic memory kernel abstract the exact controllability and observability for a heat equation with hyperbolic memory kernel in anisotropic and nonhomogeneous media are considered due to the appearance of such a kind of memory the speed of propagation for solutions to the heat equation is finite and the corresponding controllability property has a certain nature similar to hyperbolic equations and is significantly different from that of the usual parabolic equations by means of carleman estimate we establish a positive controllability and observability result under some geometric condition on the other hand by a careful construction of highly concentrated approximate solutions to hyperbolic equations with memory we present a negative controllability and observability result when the geometric condition is not satisfied

linear transformations which preserve fixed rank abstract let m m n f denote the set of all m n matrices over the algebraically closed field f let t denote a linear transformation t m m n f m m n f theorem if max m n 2 k 2 k 1 and t preserves rank k matrices i e a k implies t a k then there exist nonsingular m m and n n matrices u and v respectively such that either i t a uav for all a m m n f or ii m n and t a ua t v for all a m n f where a t denotes the transpose of a

linear operators that preserve column rank of fuzzy matrices abstract for each m 2 and n 3 we characterize the linear operators t on the m n fuzzy matrices that preserve column rank that is t preserves column rank if and only if t strongly preserves column rank 1 and it preserves column rank 3 other characterizations of column rank preserving operators are also given

on the asymptotic stability of solutions of volterra integro differential equations nonlinear differential delay equations are investigated by means of their associated semigroups conditions are found for which solutions have nonexponential decay but nevertheless behave asymptotically as an inverse power of t

stability analysis of synchronous oscillations in a weakly coupled integrodifferential system abstract it is shown that synchronous oscillations arising via a hopf bifurcation in a class of weakly coupled integrodifferential systems are destabilised by a weak difference coupling of the oscillators

blow up and global existence to a degenerate reaction diffusion equation with nonlinear memory abstract in this paper we consider a degenerate reaction diffusion equation u k t u u q 0 t u p x s d s x t 0 with homogeneous dirichlet boundary conditions where p q are nonnegative constants and 0 k 1 the blow up criteria and the blow up rate are obtained

maximal rank one spaces of matrices over chain semirings ii u i spaces abstract vectors matrices and various spaces of matrices over the boolean 0 1 algebra have been studied extensively along with their applications to graph theory the boolean 0 1 algebra has been generalized to a class of semirings called chain semirings this class includes the fuzzy interval a class of maximal relative to containment rank 1 spaces of matrices over chain semirings is identified

on a class of non linear parabolic control systems with memory effects this work establishes the local exact null controllability of non linear parabolic integrodifferential equations with non linearities under the integral sign in a bounded domain and with homogeneous dirichlet boundary conditions the control is assumed to be distributed along a subdomain of using a carleman type inequality we first prove the global exact null controllability of a linearized equation then by a fixed point method we obtain the main result for the non linear case this result asserts that when the non linearity is of class c 1 and globally lipschitz the system is null controllable

on the null controllability of heat equation with memory abstract the aim of this article is to analyze the null controllability properties of the heat equations with memory by a new carleman inequality with weighted functions that do not vanish at t 0 we prove the controllability for the system with a located internal controller under a condition on the kernel

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

a holling s type ii prey predator model with stage structure and nonlocal delay abstract in this paper a prey predator model with reaction diffusion is investigated under homogenous neumann boundary condition by taking food ingestion and species moving into account model is further coupled with holling s type ii function response and nonlocal delay sufficient conditions for the global stability of three equilibria i e positive semi trivial and trivial steady states are mainly derived by lyapunov functional respectively results show that intra specific competition benefits the coexistence of prey and predator numerical simulations are performed to illustrate the analytical results

controllability of some coupled stochastic parabolic systems with fractional order spatial differential operators by one control in the drift this paper is addressed to a study of the null approximate controllability for a class of coupled systems governed by two linear forward stochastic parabolic equations with fractional order spatial differential operators our method is based on the lebeau robbiano strategy the key is to establish a suitable observability estimate for some coupled fractional order backward stochastic parabolic systems with terminal states in finite dimensional spaces compared to deterministic coupled parabolic systems the coupling appearing in diffusion terms in the stochastic case introduces quite interesting new phenomena we present a somewhat surprising counterexample to show that the controllability of coupled stochastic parabolic systems is not robust with respect to the coupling coefficient in diffusion terms this indicates that the usual carleman type estimate approach does not seem to work for our controllability problem moreover our controllability results for parabolic systems with fractional order spatia

stabilization of semilinear heat equations with fading memory by boundary feedbacks abstract in this paper we design stabilizing dirichlet boundary feedback laws for heat equations with fading memory the linear finite dimensional controllers are easily manageable from the computational point of view because of their simple feedback form involving only the first n n eigenfunctions of the laplace operator two examples are provided at the end of the paper in order to illustrate the acquired results