necessary and sufficient conditions for near optimal harvesting control problem of stochastic age dependent system in this paper we consider a near optimal harvesting control problems for stochastic age structured population system we establish necessary and sufficient conditions for near optimality these conditions are described by adjoint equations and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases at last an example is given for illustrating our results

stationary distribution of stochastic population systems in this paper we consider the stochastic differential equation sde population model dx t diag x1 t xn t b ax t dt db t for n interacting species the main aim is to study the stationary distribution of the solution it is known see e g bahar and mao 2004 2 and mao 2005 6 if the noise intensity is sufficiently large then the population may become extinct with probability one our main aim here is to find out what happens if the noise is relatively small in this paper we will show the existence of a unique stationary distribution we will then develop a useful method to compute the mean and variance of the stationary distribution computer simulations will be used to illustrate our theory

a multi level discontinuous galerkin method for solving the stationary navier stokes equations abstract in this paper we consider the multi level discontinuous finite element method for solving the stationary incompressible navier stokes equations on the coarsest mesh the discrete nonlinear navier stokes equations are solved by using piecewise polynomial functions which are totally discontinuous across inter element boundaries and are pointwise divergence free on each element for the velocity and are continuous functions for the pressure subsequent approximations are generated on a succession of refined grids by solving the newton linearized navier stokes equations using piecewise polynomial functions which are similar to that on the coarsest mesh finally the well posedness and the optimal error estimate for the multi level discontinuous galerkin method are provided the error analysis shows that when the mesh scales k j 1 o k j 2 h j 1 o h j 2 with j 0 1 j 1 are chosen the multi level finite element method can save a large amount of computational time compared with the one level finite element method

partitioning strategies for the interaction of a fluid with a poroelastic material based on a nitsche s coupling approach abstract we develop a computational model to study the interaction of a fluid with a poroelastic material the coupling of stokes and biot equations represents a prototype problem for these phenomena which feature multiple facets on one hand it shares common traits with fluid structure interaction on the other hand it resembles the stokes darcy coupling for these reasons the numerical simulation of the stokes biot coupled system is a challenging task the need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners for the equations at hand are typical shortcomings of classical discretization methods applied to this problem such as the finite element method for spatial discretization and finite differences for time stepping the application of loosely coupled time advancing schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others at each time step in this work we develop and thoroughly analyze a loosely coupled scheme for stokes biot equations the scheme is based on nitsche s method for enforcing interface conditions once the interface operators corresponding to the interface conditions have been defined time lagging allows us to build up a loosely coupled scheme with good stability properties the stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem the error of the resulting method is also analyzed showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes in order to restore good approximation properties while maintaining the computational efficiency of the loosely coupled approach we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand

new criteria on persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching abstract this paper concerns persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching by using some novel stochastic analysis techniques sufficient criteria for the partial permanence and partial extinction are established some novel sufficient conditions on persistence in mean and extinction are also obtained nontrivial examples are provided to illustrate our results

convergence of numerical solutions to stochastic age dependent population equations with markovian switching in this paper a class of stochastic age dependent population equations with markovian switching is considered the main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age dependent population equations with markovian switching it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions an example is given for illustration

lower limits of discrete universal denoising in the spirit of results on universal compression we compare the performance of universal denoisers on discrete memoryless channels to that of the best performance obtained by an omniscient kth order sliding window denoiser namely one that is tuned to the transmitted noiseless sequence we show that the additional loss incurred in the worst case by any universal denoiser on a length n sequence grows at least like omega ck radicn where c is a constant depending on the channel parameters and the loss function this shows that for fixed k the additional loss incurred by the discrete universal denoiser dude is no larger than a constant multiplicative factor of the best possible furthermore we compare universal denoisers to denoisers that are aware of the distribution of the transmitted noiseless sequence we show that even for this weaker target loss for any universal denoiser there exists some distribution for the noiseless sequence corresponding to a sequence of independent and identically distributed i i d random variables whose optimum expected loss is lower than that incurred by the universal denoiser by omega 1 radicn

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

stationary distribution of stochastic population dynamics in state dependent random environments abstract this work studies the stationary distribution of stochastic lotka volterra population dynamics in state dependent random environments we first use the stochastic comparison approach to handle the difficulty caused by the state dependent regime switching then the ergodic property and positive recurrence are investigated by the theory of m matrix under small perturbation the mean of the stationary distribution is also estimated at last the main results are illustrated by a numerical example

the interface control domain decomposition method for stokes darcy coupling the interface control domain decomposition icdd method of discacciati gervasio and quarteroni siam j control optim 51 2013 pp 3434 3458 doi 10 1137 120890764 j coupled syst multiscale dyn 1 2013 pp 372 392 doi 10 1166 jcsmd 2013 1026 is proposed here to solve the coupling between stokes and darcy equations according to this approach the problem is formulated as an optimal control problem whose control variables are the traces of the velocity and the pressure on the internal boundaries of the subdomains that provide an overlapping decomposition of the original computational domain a theoretical analysis is carried out and the well posedness of the problem is proved under certain assumptions on both the geometry and the model parameters an efficient solution algorithm is proposed and several numerical tests are implemented our results show the accuracy of the icdd method its computational efficiency and robustness with respect to the different parameters involved grid siz

hierarchical universal coding in an earlier paper we proved a strong version of the redundancy capacity converse theorem of universal coding stating that for most sources in a given class the universal coding redundancy is essentially lower bounded by the capacity of the channel induced by this class since this result holds for general classes of sources it extends rissanen s 1986 strong converse theorem for parametric families while our earlier result has established strong optimality only for mixture codes weighted by the capacity achieving prior our first result herein extends this finding to a general prior for some cases our technique also leads to a simplified proof of the above mentioned strong converse theorem the major interest in this paper however is in extending the theory of universal coding to hierarchical structures of classes where each class may have a different capacity in this setting one wishes to incur redundancy essentially as small as that corresponding to the active class and not the union of classes our main result is that the redundancy of a code based on a two stage mixture first within each class and then over the classes is no worse than that of any other code for most sources of most classes if in addition the classes can be efficiently distinguished by a certain decision rule then the best attainable redundancy is given explicitly by the capacity of the active class plus the normalized negative logarithm of the prior probability assigned to this class these results suggest some interesting guidelines as for the choice of the prior we also discuss some examples with a natural hierarchical partition into classes

stochastic kolmogorov type system with infinite delay abstract the paper considers a stochastic functional kolmogorov type population system with infinite delay under the general probability measures main aim is to show that the environment noise will not only suppress a potential population explosion but also make the solution be stochastically ultimately bounded and asymptotic stable moreover two stochastic functional lotka volterra equations as examples are provided to illustrate the main results

a domain decomposition method for the steady state navier stokes darcy model with beavers joseph interface condition this paper proposes and analyzes a robin type multiphysics domain decomposition method ddm for the steady state navier stokes darcy model with three interface conditions in addition to the two regular interface conditions for the mass conservation and the force balance the beavers joseph condition is used as the interface condition in the tangential direction the major mathematical difficulty in adopting the beavers joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system y cao et al comm math sci 8 2010 pp 1 25 y cao et al siam j numer anal 47 2010 pp 4239 4256 in this paper the well posedness of the navier stokes darcy model with beavers joseph condition is analyzed by using a branch of nonsingular solutions by following the idea in y cao et al numer math 117 2011 pp 601 629 the three physical interface conditions are utilized together to construct the robin type boundary conditions on th

construction of positivity preserving numerical method for stochastic age dependent population equations the aim of this paper is to construct a numerical method preserving positivity for stochastic age dependent population equations we use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution it is proved that the balanced implicit method bim preserves positivity and converges with strong order 1 2 under given conditions finally two examples are simulated to verify the positivity and efficiency of the proposed method

a stochastic model of aids and condom use in this paper we introduce stochasticity into a model of aids and condom use via the technique of parameter perturbation which is standard in stochastic population modelling we show that the model established in this paper possesses non negative solutions as desired in any population dynamics we also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system

convergence of numerical solutions to stochastic age structured population system with diffusion in this paper stochastic age structured population system with diffusion are studied in general most of stochastic age structured population system with diffusion do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution

asymptotic stability of stochastic age dependent population equations with markovian switching the main aim of this paper is to discuss the almost surely asymptotic stability of the stochastic age dependent population equations with markovian switching an example will be discussed to illustrate the theory

existence and uniqueness attraction for stochastic age structured population systems with diffusion and poisson jump in this paper the problems about the existence and uniqueness attraction for strong solution of stochastic age structured population systems with diffusion and poisson jump are considered under the non lipschitz condition with the lipschitz condition being considered as a special case the existence and uniqueness for such systems is firstly proved by using the burkholder davis gundy inequality b d g inequality and ito s formula and then by using a novel inequality technique some sufficient conditions ensuring the existence for the domain of attraction are established as another by product the exponential stability in mean square moment of strong solution for such systems can be also discussed

stochastic lotka volterra population dynamics with infinite delay we discover in this paper that when environmental noise is strongly dependent on the population size this noise may suppress the population explosion in a finite time and guarantee the global positive solution when the environmental noise is weakly dependent on the population size the conditions that guarantee the global positive solution are independent of this environmental noise we also discuss the pth moment boundedness stochastic ultimate boundedness and moment average boundedness in time under two classes of conditions these properties are natural requirements from the biological point of view

numerical solution of the stationary navier stokes equations using a multilevel finite element method the numerical implementation of a multilevel finite element method for the steady state navier stokes equations is considered the multilevel method proposed here for the navier stokes equations is a multiscale method in which the full nonlinear navier stokes equations are only solved on a single coarse grid subsequent approximations are generated on a succession of refined grids by solving a linearized navier stokes problem two numerical examples are considered the first is an example for which an exact solution is known and the second is the driven cavity problem we demonstrate numerically that for an appropriate choice of grids a two or three level finite element method is significantly more efficient than the standard one level finite element method

existence and uniqueness of global weak solutions to a cahn hilliard stokes darcy system for two phase incompressible flows in karstic geometry abstract we study the well posedness of a coupled cahn hilliard stokes darcy system which is a diffuse interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry existence of finite energy weak solution that is global in time is established in both 2d and 3d weak strong uniqueness property of the weak solutions is provided as well

persistence attractivity and delay in facultative mutualism abstract relations between persistence and ultimate boundedness of the solutions of the lotka volterra system dx t dt x t r 1 a 11 x t a 22 y t dy t dt y t r 2 a 21 x t a 22 y t modelling facultative mutualism with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system

discrete denoising with shifts we introduce s dude a new algorithm for denoising discrete memoryless channel dmc corrupted data the algorithm which generalizes the recently introduced dude discrete universal denoiser aims to compete with a genie that has access in addition to the noisy data also to the underlying clean data and that can choose to switch up to m times between sliding window denoisers in a way that minimizes the overall loss when the underlying data form an individual sequence we show that the s dude performs essentially as well as this genie provided that m is sublinear in the size of the data when the clean data are emitted by a piecewise stationary process we show that the s dude achieves the optimum distribution dependent performance provided that the same sublinearity condition is imposed on the number of switches to further substantiate the universal optimality of the s dude we show that when the number of switches is allowed to grow linearly with the size of the data any sequence of scheme s fails to compete in the above sense using dynamic programming we derive an efficient implementation of the s dude which has complexity time and memory growing linearly with the data size and the number of switches m preliminary experimental results are presented suggesting that s dude has the capacity to improve on the performance attained by the original dude in applications where the nature of the data abruptly changes in time or space as is often the case in practice

stochastic differential delay equations of population dynamics in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

global stability of a stochastic predator prey system with infinite delays abstract this paper is concerned with the global asymptotic stability of a stochastic delay predator prey system with beddington deangelis functional response sufficient criteria for the global asymptotic stability of the system are established some simulation figures are provided to show that our model is more realistic than existing models

exponential stability of numerical solutions to stochastic age dependent population equations the main aim of this paper is to consider the exponential stability of the euler maruyama scheme for a class of stochastic age dependent population equation the definition of exponential stability of numerical methods is established the conditions under which the method is exponentially stable in mean square are determined

parallel two grid finite element method for the time dependent natural convection problem with non smooth initial data abstract in this paper we consider the parallel two grid finite element method for the transient natural convection problem with non smooth initial data our numerical scheme involves solving a nonlinear natural convection problem on the coarse grid and solving a linear natural convection problem on the fine grid the linear natural convection problem can be split into two subproblems which can be solved in parallel a linearized navier stokes problem and a linear parabolic problem we firstly provide the stability and convergence of standard galerkin finite element method with non smooth initial data secondly we develop optimal error estimates of two grid finite element method for velocity and temperature in h 1 norm and for pressure in l 2 norm in order to overcome the difficulty posed by the loss of regularity some suitable weight functions are introduced in our stability and convergence analysis for the natural convection equations finally some numerical results are presented to verify the established theoretical results

stability and moment boundedness of an age structured model with randomly varying immigration or harvesting abstract in this paper we study the stability and moment boundedness of the solutions to the linear age structured model with randomly varying immigration or harvesting for this model we study stability and the asymptotic behavior of the first moment and the results are identical to that of the corresponding deterministic age structured model and the linear age structured model with the white noise however the stability and boundedness of the second moment are complicated and depend on the randomly varying immigration or harvesting for the linear age structured model with randomly varying immigration or harvesting we directly prove that the second moment m t a is bounded for 0 t a when t a 0 using the laplace transform in the framework of ito doob integral we give the explicit expressions of the second moments m t 0 and m t a and then establish the sufficient conditions for the second moments to be bounded and unbounded respectively through the supreme of the real parts of all characteristic roots we also study the asymptotic behaviors of the second moments m t 0 and m t a and give the sufficient condition for stochastically ultimately boundedness of the model

a modified two grid decoupling method for the mixed navier stokes darcy model in this paper a modified two grid decoupling method for the mixed navier stokes darcy model is proposed and analyzed the solution on interface condition is approximated by the solution obtained on the fine grid stability and convergence of the method are proved the convergence rate for the l 2 norm of u and p is improved from o h 3 2 to o h 2 the numerical results are consistent with the theoretical results and illustrate that the proposed method is quite efficient

numerical analysis of the balanced implicit method for stochastic age dependent capital system with poisson jumps abstract the aim of this paper is to construct a numerical method to preserve positivity and mean square dissipativity of stochastic age dependent capital system with poisson jumps we use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution it is proved that the balanced implicit method bim preserves positivity and converges with order 1 2 under given conditions in addition some sufficient conditions are obtained for ensuring the system and the balanced implicit method bim are mean square dissipative finally a numerical example is simulated to illustrate the efficiency of theoretical results

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

universal filtering via prediction we consider the filtering problem where a finite alphabet individual sequence is corrupted by a discrete memoryless channel and the goal is to causally estimate each sequence component based on the past and present noisy observations we establish a correspondence between the filtering problem and the problem of prediction of individual sequences which leads to the following result given an arbitrary finite set of filters there exists a filter which performs with high probability essentially as well as the best in the set regardless of the underlying noiseless individual sequence we use this relationship between the problems to derive a filter guaranteed of attaining the finite state filterability of any individual sequence by leveraging results from the prediction problem

exponential stability of numerical solutions for a class of stochastic age dependent capital system with poisson jumps recently numerical solutions of stochastic differential equations have received a great deal of attention numerical approximation schemes are invaluable tools for exploring their properties in this paper we introduce a class of stochastic age dependent vintage capital system with poisson jumps we also give the discrete approximate solution with an implicit euler scheme in time discretization using gronwall s lemma and barkholder davis gundy s inequality some criteria are obtained for the exponential stability of numerical solutions to the stochastic age dependent capital system with poisson jumps it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions where information on the order of approximation is provided these error bounds imply strong convergence as the timestep tends to zero a numerical example is used to illustrate the theoretical results

absolute stability analysis in cellular neural networks with variable delays and unbounded delay abstract in this paper the existence and uniqueness of the equilibrium point and absolute stability of a class of cellular neural networks with globally lipschitz continue activation functions are investigated the neural networks contain both variable and unbounded delays the necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained by constructing proper vector liapunov functions nonlinear integrodifferential inequalities involving both variable delays and unbounded delay which are corresponding to the neural networks are established by using m matrix theory and qualitative property of the integrodifferential inequalities the sufficient conditions for absolute stability global asymptotic stability are obtained

a multilevel mesh independence principle for the navier stokes equations multilevel finite element discretization methods for the navier stokes equations are considered in contrast to usual multilevel methods a superlinear scaling of the consecutive meshwidths h j 1 mathcal o h j alpha j is used on the coarsest mesh the discretized system is solved which is small and nonlinear on each subsequent mesh only one or two newton correction steps are performed so that only one or two larger linear systems are solved the scalings of the meshwidths that lead to optimal accuracy of the approximate solution in both the h 1 and l 2 norm are investigated an error analysis of independent interest is also presented for the basic finite element method using the conservation form of the nonlinear term this formulation leads to a nonlinear system whose nonlinearity is easier to resolve than the systems arising when either the convective or explicitly skew symmetric corms are used for the nonlinear term

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

a two grid method based on newton iteration for the navier stokes equations in this paper we consider a two grid method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations we prove the convergence rate of the approximation obtained by this method the two grid method involves solving one small nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right hand side the algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any reynolds number numerical example is given to show the convergence of the method

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

stochastic stabilization and destabilization it is shown in this paper that any nonlinear systems dot x t f x t t in rd can be stabilized by brownian motion provided f hook x t k x for some k 0 on the other hand this system can also be destabilized by brownian motion if the dimension d 2 similar results are also obtained for any given stochastic differential equation dx t f hook x t t g x t t dw t

the existence and asymptotic behaviour of energy solutions to stochastic age dependent population equations driven by levy processes in this paper we introduce a class of stochastic age dependent population equations driven by levy processes existence and uniqueness of energy solutions for stochastic age dependent population dynamic system are proved under lipschitz condition in hilbert space the moment boundedness of the approximate solution by the galerkin method is considered we discuss by using the energy equality the exponential stability theorems of the energy solution to stochastic age dependent population equations

age distribution dynamics with stochastic jumps in mortality while deterministic age distribution models have been extensively studied and applied in various disciplines little work has been devoted to understanding the role of stochasticity in birth and mortality terms in this paper we analyse a stochastic m kendrick von foerster equation in which jumps in mortality represent intense losses of population due to external events we present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments we also derive the dynamics of the mean age of the population and its harmonic mean the framework is then used to calculate the age distribution of salt in the soil root zone where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events

twice universal denoising we propose a sequence of universal denoisers motivated by the goal of extending the notion of twice universality from universal data compression theory to the sliding window denoising setting given a sequence length n and a denoiser the kth order regret of the latter is the maximum excess expected denoising loss relative to sliding window denoisers with window length 2k 1 where for a given clean sequence the expectation is over all channel realizations and the maximum is over all clean sequences of length n we define the twice universality penalty of a denoiser as its excess kth order regret when compared to a bound on the kth order regret of the denoising algorithm dude with parameter k and we are interested in denoisers with a negligible penalty for all k simultaneously we consider a class of denoisers that apply one of a number of constituent denoisers based on minimizing an estimated denoising loss and establish a formal relationship between the error in the estimated denoising loss and the twice universality penalty of the resulting denoiser given a sequence of window parameters kn increasing in n sufficiently fast we use this approach to construct and analyze a specific sequence of denoisers that achieves a much smaller twice universality penalty for k kn than the sequence of dude denoisers with parameter kn

numerical analysis for stochastic age dependent population equations with poisson jumps in this paper stochastic age dependent population equations with poisson jumps are considered in general most of stochastic age dependent population equations with jumps do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the main purpose of this paper is to develop a numerical euler scheme and show the convergence of the numerical approximation solution to the true solution

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

convergence of the semi implicit euler method for stochastic age dependent population equations abstract a class of semi implicit methods is introduced for stochastic age dependent population equations it is proved that the semi implicit euler methods are convergent with strong order p 1 2 an example is given to illustrate the efficiency of the semi implicit euler method

on the solution of the coupled navier stokes and darcy equations abstract this paper introduces and analyzes two mathematical models for coupling the incompressible navier stokes equations with the porous media flow equations a numerical method that uses continuous finite elements in the incompressible flow region and discontinuous finite elements in the porous medium is proposed existence and uniqueness results under small data condition of the numerical solution are proved optimal a priori error estimates are derived numerical examples comparing the two models under varying physical parameters are provided

analysis of a mixed finite element method for a cahn hilliard darcy stokes system in this paper we devise and analyze a mixed finite element method for a modified cahn hilliard equation coupled with a nonsteady darcy stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock copolymer melts the time discretization is based on a convex splitting of the energy of the equation we prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system and unconditionally uniquely solvable we prove that the discrete phase variable is bounded in l infty left 0 t l infty right and the discrete chemical potential is bounded in l infty left 0 t l 2 right for any time and space step sizes in two and three dimensions and for any finite final time t we subsequently prove that these variables converge with optimal rates in the appropriate energy norms in both two and three dimensions

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

permanence and extinction for a single species system with jump diffusion abstract in this study we consider the effect of jump diffusion random environmental perturbations on the permanence and extinction of a single species dispersal periodic system in poor patchy environments with the possibility of species loss during their dispersion among patches first we prove that there is a unique global positive solution to the system with any initial positive value with probability 1 and we obtain the sufficient conditions that stochastically ensure the ultimate boundedness as well as the asymptotic polynomial growth of the population system next we establish the sufficient conditions for the almost sure permanence in the mean stochastic permanence and extinction of the system in particular by constructing an appropriate integrating factor we obtain the sufficient conditions for the almost sure weak permanence of the patch the conditions obtained for permanence generalize the sufficient conditions established previously on the system without random environmental perturbations finally we discuss the biological implications of the main results

tamed em scheme of neutral stochastic differential delay equations abstract in this paper we investigate the convergence of the tamed euler maruyama em scheme for a class of neutral stochastic differential delay equations the strong convergence results of the tamed em scheme are presented under global and local non lipschitz conditions respectively moreover under the global lipschitz condition we provide the convergence rate of tamed em scheme which could be the same as the convergence rate of classical em scheme one half

numerical analysis for stochastic age dependent population equations a numerical method proposed to approximate the solution of a class of stochastic age dependent populations we show that under certain conditions weaker than linear growth and global lips chits the euler scheme applied to stochastic age dependent population converges to the analytic solution and provide information on the order of approximation

existence uniqueness and exponential stability for stochastic age dependent population in this paper we introduce a class of stochastic age dependent population dynamic system existence and uniqueness of strong solution are proved for stochastic age dependent population dynamic system in hilbert space using klmogorou s inequality and barkholder davis gundy s lemma some criteria are obtained for the exponential stability of stochastic age dependent population dynamic system

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

numerical solution to a mixed navier stokes darcy model by the two grid approach we study numerical methods for a coupled navier stokes darcy model which describes a fluid flow filtrating through porous media a decoupled and linearized two grid algorithm is proposed numerical analysis and experiments are presented to show the efficiency and effectiveness of the decoupled and linearized algorithm

a two grid decoupling method for the mixed stokes darcy model in this paper we consider the mixed stokes darcy problem which describes a fluid flow coupled with a porous media we present a modified two grid method for decoupling this mixed model stability is proved and optimal error estimates are derived the numerical results show that the modified two grid method is effective and has the same accuracy as the coupling scheme when we choose h h 2

a multigrid method for viscoelastic fluid flow we study a multigrid finite element method for a viscoelastic fluid flow obeying an oldroyd b type constitutive law the multigrid method is a time saving method in which the full nonlinear system is solved on a coarse grid and subsequent approximations are generated on a succession of refined grids by solving a linearized problem we show that the linearized problem has an approximate solution and present an error bound for a two grid method we also numerically demonstrate that the multigrid method is significantly more efficient than the standard one grid finite element method

convergence of numerical solutions to stochastic age structured population equations with diffusions and markovian switching in this paper it is considered for a class of stochastic age structured population equations with diffusions and markovian switching most kind of equations are nonlinear and cannot be solved explicitly so the construction of efficient computational methods is of great importance the main aim of this paper is to develop a numerical scheme and investigate the convergence of numerical approximation an example is given for illustration

robin robin domain decomposition methods for the steady state stokes darcy system with the beavers joseph interface condition domain decomposition methods for solving the coupled stokes darcy system with the beavers joseph interface condition are proposed and analyzed robin boundary conditions are used to decouple the stokes and darcy parts of the system then parallel and serial domain decomposition methods are constructed based on the two decoupled sub problems convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence

convergence of numerical solutions for a class of stochastic age dependent capital system with random jump magnitudes in stochastic differential equations sdes there is a class of stochastic functional differential equations with random jump magnitudes which aries in many financial models in general most equations of stochastic age dependent capital system do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties in this paper the numerical approximation is established for a class of stochastic age dependent capital system with random jump magnitudes the main aim of this paper is to investigate the convergence of the numerical approximation for a class of stochastic age dependent capital system with random jump magnitudes it is proved that the numerical approximate solutions converge to the analytical solutions of the equations under given conditions the numerical approximate results in zhang et al 2011 2 are improved an example is given for illustration

practical exponential stability of stochastic age dependent capital system with levy noise abstract it is well known that stability is one of most important topics in economy and control in this paper we focus on the practical stability problem for a class of stochastic age dependent vintage capital system with levy noise compared with the classical lyapunov stability theory practical stability can depict not only qualitative behavior but also quantitative properties such as specific trajectory bounds and specific transient behavior with the help of the stochastic analysis theory and ito s formula we establish some novel criteria for the mean square and almost sure practical exponential stability of the addressed system the obtained results improve some previous works given in the literature moreover an example is provided to illustrate the theoretical results

lifetime and reproduction of a marked individual in a two species competition process the interest is in a stochastic model for the competition of two species which was first introduced by reuter 18 and iglehart 11 and then analyzed by ridler rowe 19 the model is related to the two species autonomous competitive model zeeman 24 where individuals compete either directly or indirectly for a limited food supply and consequently birth and death rates depend on the population size of one or both of the species the aim is to complement the treatment of the model we started in 8 9 by focusing here on probabilistic descriptors that are inherently linked to an individual its residual lifetime and the number of direct descendants we present an approximating model based on the maximum size distribution and we discuss on various models defined in terms of the underlying killing and reproductive strategies numerical examples are presented to show the effects of the killing and reproductive strategies on the behavior of an individual and how the impact of these strategies on the descriptors vanishes in highly competitive ecosystems

convergence of the split step θ method for stochastic age dependent population equations with poisson jumps in this paper a new split step ss method for stochastic age dependent population equations with poisson jumps is constructed the main aim of this paper is to investigate the convergence of the ss method for stochastic age dependent population equations with poisson jumps it is proved that the proposed method is convergent with strong order 1 2 under given conditions finally an example is simulated to verify the results obtained from theory the results show that the ss method has better accuracy compared to the euler method

exponential stability of numerical solutions to a stochastic age structured population system with diffusion the main aim of this paper is to investigate the exponential stability of the euler method for a stochastic age structured population system with diffusion the definition of exponential mean square stability of numerical method is introduced it is proved that the euler scheme is exponentially stable in mean square sense an example is given for illustration

a two grid method of a mixed stokes darcy model for coupling fluid flow with porous media flow we study numerical methods for solving a coupled stokes darcy problem in porous media flow applications a two grid method is proposed for decoupling the mixed model by a coarse grid approximation to the interface coupling conditions error estimates are derived for the proposed method both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two grid approach for solving multimodeling problems potential extensions and future directions are discussed

convergence of numerical solutions to stochastic age structured system of three species abstract in general most of stochastic age structured system of three species do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age structured system of three species

convergence of numerical solutions to stochastic age dependent population equations in this paper stochastic age dependent population equations one of the important classes of hybrid systems are studied in general most of stochastic age dependent population equations do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution

dg approximation of coupled navier stokes and darcy equations by beaver joseph saffman interface condition in this work we couple the incompressible steady navier stokes equations with the darcy equations by means of the beaver joseph saffman s condition on the interface under suitable smallness conditions on the data we prove existence of a weak solution as well as some a priori estimates we establish local uniqueness when the data satisfy additional smallness restrictions then we propose a discontinuous galerkin scheme for discretizing the equations and do its numerical analysis

a multilevel decoupled method for a mixed stokes darcy model this paper studies decoupled numerical methods for a mixed stokes darcy model for coupling fluid and porous media flows a two level algorithm is proposed and analyzed in mu and xu 2007 10 we generalize the two level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm the multilevel algorithm solves the mixed stokes darcy system by applying efficient legacy code for single model solvers to solve two decoupled stokes and darcy subproblems on all the subsequently refined meshes except for a much smaller global problem only on a very coarse initial mesh numerical experiments are conducted for both the two level and multilevel algorithms to illustrate their effectiveness and efficiency and validate the related theoretical analysis

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

a multilevel decoupling method for the navier stokes darcy model abstract this paper considers a multilevel decoupling method for the coupled navier stokes darcy model describing a free flowing fluid over a porous medium the method utilizes a sequence of meshes on which a low dimensional fully coupled nonlinear problem is solved only on a very coarse initial mesh on subsequent finer meshes the approximate solution in each flow region is obtained by solving a linear decoupled problem and performing a correction step the correction step in each domain is achieved by solving a linear system that differs from the original decoupled system only in the right hand side we prove optimal error estimates and demonstrate that for a sequence of meshes with spacing h j h j 1 2 the decoupling method is computationally efficient and achieves the same order of approximation as the fully coupled method

some new results of nonautonomous lotka volterra competitive systems with delays abstract in this paper we improve and generalize the results of montes de oca and zeeman j math anal appl 192 1995 360 370 proc amer math soc 124 1996 3677 3687 to general n species nonautonomous lotka volterra type competitive systems with finite or infinite delays we establish a series of criteria under which a part of the n species of the systems is driven to extinction while the remaining part of the n species is persistent or uniformly persistent or coexists globally asymptotically stable

a dual porosity stokes model and finite element method for coupling dual porosity flow and free flow in this paper we propose and numerically solve a new model considering confined flow in dual porosity media coupled with free flow in embedded macrofractures and conduits such situation arises for example for fluid flows in hydraulic fractured tight shale oil gas reservoirs the flow in dual porosity media which consists of both matrix and microfractures is described by a dual porosity model and the flow in the macrofractures and conduits is governed by the stokes equation then the two models are coupled through four physically valid interface conditions on the interface between dual porosity media and macrofractures conduits which play a key role in a physically faithful simulation with high accuracy all the four interface conditions are constructed based on fundamental properties of the traditional dual porosity model and the well known stokes darcy model the weak formulation is derived for the proposed model and the well posedness of the model is analyzed a finite element semidiscretizati