global attractor of a coupled finite difference reaction diffusion system with delays abstract in the study of asymptotic behavior of solutions for reaction diffusion systems an important concern is to determine whether and when the system has a global attractor which attracts all positive time dependent solutions the aim of this paper is to investigate the global attraction problem for a finite difference system which is a discrete approximation of a coupled system of two reaction diffusion equations with time delays sufficient conditions are obtained to ensure the existence and global attraction of a positive solution of the corresponding steady state system applications are given to three types of lotka volterra reaction diffusion models where time delays may appear in the opposing species

biset transformations of tambara functors abstract if we are given an h g biset u for finite groups g and h then any mackey functor on g can be transformed by u into a mackey functor on h in this article we show that the biset transformation is also applicable to tambara functors when u is right free and in fact forms a functor between the category of tambara functors on g and h this biset transformation functor is compatible with some algebraic operations on tambara functors such as ideal quotients or fractions in the latter part we also construct the left adjoint of the biset transformation

the spectrum of the burnside tambara functor on a finite cyclic p group abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this analogy previously we have defined an ideal of a tambara functor in this article we calculate the prime spectrum of the burnside tambara functor when g is a finite cyclic p group for a prime integer p

tambarization of a mackey functor and its application to the witt burnside construction abstract for an arbitrary group g a semi mackey functor is a pair of covariant and contravariant functors from the category of g sets and is regarded as a g bivariant analog of a commutative semi group in this view a g bivariant analog of a semi ring should be a semi tambara functor a tambara functor is firstly defined by tambara which he called a tnr functor when g is finite as shown by brun a tambara functor plays a natural role in the witt burnside construction it will be a natural question if there exist sufficiently many examples of tambara functors compared to the wide range of mackey functors in the first part of this article we give a general construction of a tambara functor from any mackey functor on an arbitrary group g in fact we construct a functor from the category of semi mackey functors to the category of tambara functors this functor gives a left adjoint to the forgetful functor and can be regarded as a g bivariant analog of the monoid ring functor in the latter part when g is finite we investigate relations with other mackey functorial constructions crossed burnside ring elliott s ring of g strings jacobson s f burnside ring all these lead to the study of the witt burnside construction

general relaxation methods for initial value problems with application to multistep schemes recently an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial value problems using runge kutta methods we generalize this approach to multistep methods including all general linear methods of order two or higher and many other classes of schemes we prove the existence of a valid relaxation parameter and high order accuracy of the resulting method in the context of general equations including but not limited to conservative or dissipative systems the theory is illustrated with several numerical examples

numerical methods for systems of nonlinear parabolic equations with time delays abstract the purpose of this paper is to investigate some numerical aspects of a class of coupled nonlinear parabolic systems with time delays the system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations the mathematical analysis of the nonlinear system is by the method of upper and lower solutions and its associated monotone iterations three monotone iterative schemes are presented and it is shown that the sequence of iterations from each one of these iterative schemes converges monotonically to a unique solution of the finite difference system a theoretical comparison result for the various monotone sequences and error estimates for the three monotone iterative schemes are obtained it is also shown that the finite difference solution converges to the classical solution of the parabolic system as the mesh size decreases to zero

symmetric positive solutions to singular system with multi point coupled boundary conditions in this paper we study the existence and multiplicity of symmetric positive solutions for a nonlinear system with multi point coupled boundary conditions the arguments are based upon a specially constructed cone and the fixed point index theorem in cones an example is then given to demonstrate the applicability of our results

ideals of tambara functors abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this article we consider a g bivariant analog of the ideal theory for tambara functors

qualitative analysis of a coupled reaction diffusion model in biology with time delays abstract certain biochemical reaction can be modeled by a coupled system of time delayed ordinary differential equations and linear parabolic partial differential equations in a three compartment model these equations are coupled through the boundary conditions the aim of this paper is to give a qualitive analysis of this unusual coupled system the analysis includes the existence and uniqueness of a global solution explicit upper and lower bounds of the solution and global stability of a steady state solution the global stability result is with respect to any nonnegative initial perturbation and is independent of the time delays in the process of reaction special attention is given to the goodwin model for biochemical control of genes by a negative feedback mechanism with time delay and diffusion

estimate of solutions for differential and difference functional equations with applications to difference methods abstract the theorems on the estimate of solutions for nonlinear second order partial differential functional equations mainly of parabolic type with dirichlet s condition and for the suitable explicit finite difference functional schemes are proved the proofs are based on the comparison technique the convergent difference method given is considered without an assumption of the global generalized perron condition on the functional variable but with local one in some sense only it is a consequence of our estimate theorems the functional dependence is of the volterra type

accelerated monotone iterative methods for finite difference equations of reaction diffusion this paper is concerned with numerical methods for a finite difference system of reaction diffusion convection equation under nonlinear boundary condition various monotone iterative methods are presented and each of these methods leads to an existence comparison theorem as well as a computational algorithm for numerical solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function application is given to a model problem from chemical engineering and some numerical results including a test problem with known analytical solution are presented to illustrate the various rates of convergence of the iterations

combined iterative methods for numerical solutions of parabolic problems with time delays we study monotone iterative schemes for finite difference solutions of reaction diffusion systems with time delays in this paper we derive two modified iterative schemes by combing the method of upper lower solutions and the jacobi method or the gauss seidel method the convergence and stability of the monotone iterative schemes are also discussed

harmless delays for permanence in a class of population models with diffusion effects abstract this paper studies a class of time delay reaction diffusion systems modeling the dynamics of single or interacting populations in the logistic equation we prove that when the magnitude of the instantaneous term is larger than that of the delay terms the population growthuhas the same asymptotic limit as in the case of no delay for the predator prey model a condition on the interaction rates is given to ensure the permanence effect in the ecosystem regardless of the length of delay intervals a permanence condition is also obtained in then species competition system with time delays it is shown that when the natural growth rate a1 a2 an is in an unbounded parameter set the reaction diffusion system has a positive global attractor finally long term behavior of the solutions for those time delay systems is numerically demonstrated through finite difference approximations and compared with the corresponding systems without delays

higher order compact finite difference method for systems of reaction diffusion equations this paper is concerned with a compact finite difference method for solving systems of two dimensional reaction diffusion equations this method has the accuracy of fourth order in both space and time the existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term three monotone iterative algorithms are provided for solving the resulting discrete system efficiently and the sequences of iterations converge monotonically to a unique solution of the system a theoretical comparison result for the various monotone sequences is given the convergence of the finite difference solution to the continuous solution is proved and richardson extrapolation is used to achieve fourth order accuracy in time an application is given to an enzyme substrate reaction diffusion problem and some numerical results are presented to demonstrate the high efficiency and advantages of this new approach

multiplicativity of the idempotent splittings of the burnside ring and the g sphere spectrum abstract we provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the g equivariant sphere spectrum including their hill hopkins ravenel norms where g is any finite group our results describe explicitly how these structures depend on the subgroup lattice and conjugation in g algebraically our analysis characterizes the multiplicative transfers on the localization of the burnside ring of g at any idempotent element which is of independent interest to group theorists as an application we obtain an explicit description of the incomplete sets of norm functors which are present in the idempotent splitting of the equivariant stable homotopy category

relaxation runge kutta methods fully discrete explicit entropy stable schemes for the compressible euler and navier stokes equations the framework of inner product norm preserving relaxation runge kutta methods d i ketcheson siam j numer anal 57 2019 pp 2850 2870 is extended to general convex quantities conservat

highly efficient invariant conserving explicit runge kutta schemes for nonlinear hamiltonian differential equations abstract a unified framework of invariant conserving explicit runge kutta schemes for the nonlinear hamiltonian odes and pdes are proposed by utilizing the invariant energy quadratization technique first the nonlinear hamiltonian differential equation is transformed into an equivalent reformulation which admits a quadratic energy invariant for the nonlinear ode the reformulation is then discretized using a class of relaxation runge kutta schemes for the nonlinear pde the reformulation is first discretized in the space direction by adopting the fourier pseudo spectral discretization which preserves the semi discrete quadratic conservation laws then the semi discrete system is integrated in the time direction using the explicit relaxation runge kutta method the obtained method can conserve different quadratic conservation laws to machine accuracy which improves the numerical stability during long time computations besides the proposed method keeps the same convergence rate of the standard runge kutta scheme when computed with time step size rescaling and gives a rate of convergence reduced by at most one when computed without step size rescaling numerical experiments for several odes and pdes are provided to illustrate the advantages of the proposed algorithms over long time and verify the theoretical analysis

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

asymptotic behavior of solutions for finite difference equations of reaction diffusion abstract the method of upper lower solutions and the associated existence comparison theorem for continuous reaction diffusion equations are extended to a finite difference system which is a discrete version of the continuous problem of either parabolic type or elliptic type under appropriate boundary condition it is shown by using the existence comparison theorem for the discrete system that for a certain class of initial functions the corresponding time dependent solution converges monotonically to a steady state solution this monotone convergence leads to the stability property of the steady state solution as well as an estimate of the stability region in the framework of the finite difference system numerical results are given for an enzyme substrate reaction model where multiple steady state solutions exist for a certain range of physical parameters in this situation the time dependent solution converges either to the maximal solution or to the minimal solution depending on the corresponding initial function

on the andre quillen homology of tambara functors abstract we lift to equivariant algebra three closely related classical algebraic concepts abelian group objects in augmented commutative algebras derivations and kahler differentials we define mackey functor objects in the category of tambara functors augmented to a fixed tambara functor r and we show that the usual square zero extension gives an equivalence of categories between these mackey functor objects and ordinary modules over r we then describe the natural generalization to tambara functors of a derivation building on the intuition that a tambara functor has products twisted by arbitrary finite g sets and we connect this to square zero extensions in the expected way finally we show that there is an appropriate form of kahler differentials which satisfy the classical relation that derivations out of r are the same as maps out of the kahler differentials

the crossed burnside rings iii the dress construction for a tambara functor abstract we discuss the dress construction for a tambara functor associated to a finite commutative monoid with action of a finite group

comparison between some explicit and implicit difference schemes for hamilton jacobi functional differential equations abstract initial boundary value problems of dirichlet type for first order partial functional differential equations are considered explicit difference schemes and implicit difference methods are investigated sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented it is proved that assumptions on the regularity of given functions are the same for both the methods it is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for implicit methods there are implicit difference schemes which are convergent and corresponding explicit difference methods are not convergent error estimates for both the methods are constructed numerical examples are presented

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

time delayed finite difference reaction diffusion systems with nonquasimonotone functions this paper is concerned with finite difference solutions of a system of reaction diffusion equations with coupled nonlinear boundary conditions and time delays the reaction functions and the boundary functions are not necessarily quasimonotone and the time delays may appear in the reaction functions as well as in the boundary functions the investigation is devoted to the finite difference system for both the time dependent problem and its corresponding steady state problem some monotone iteration processes for the finite difference systems are given and the asymptotic behavior of the time dependent solution in relation to the steady state solution is discussed the asymptotic behavior result leads to some local and global attractors of the time dependent problem including the convergence of the time dependent solution to a unique steady state solution an application and some numerical results to an enzyme substrate reaction diffusion problem are given all the results are directly applicable to parabolic ordinary systems and to reaction diffusion systems without time delays

numerical solutions of a three competition lotka volterra system abstract this paper is concerned with finite difference solutions of a lotka volterra reaction diffusion system with three competing species the reaction diffusion system is discretized by the finite difference method and the investigation is devoted to the finite difference system for the time dependent solution and its asymptotic behavior in relation to the corresponding steady state problem three monotone iterative schemes for the computation of the time dependent solution are presented and the sequences of iterations are shown to converge monotonically to a unique positive solution also discussed is the asymptotic behavior of the time dependent solution in relation to various steady state solutions a simple condition on the competing rate constants is obtained which ensures that for every nontrivial nonnegative initial function the corresponding time dependent solution converges either to a unique positive steady state solution or to one of the semitrivial steady state solutions the above results lead to the coexistence and permanence of the competing system as well as computational algorithms for numerical solutions some numerical results from these computational algorithms are given all the conclusions for the reaction diffusion equations are directly applicable to the finite difference solution of the corresponding ordinary differential system

difference methods for parabolic equations with robin condition abstract classical solutions of nonlinear second order partial differential functional equations of parabolic type with the robin condition are approximated in the paper by solutions of associated boundedness preserving implicit difference functional equations it is proved that the discrete solutions uniquely exist they are uniformly bounded with respect to meshes and the numerical method is convergent and stable we also find the error estimate and its asymptotic behavior the properties of some auxiliary nonlinear discrete recurrent equations are showed the proofs are based on the comparison technique and the banach fixed point theorem

fully discrete explicit locally entropy stable schemes for the compressible euler and navier stokes equations abstract recently relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation here we generalize this approach to guarantee local entropy inequalities for finitely many convex functionals entropies and apply the resulting methods to the compressible euler and navier stokes equations based on the unstructured h p adaptive ssdc framework of entropy conservative or dissipative semidiscretizations using summation by parts and simultaneous approximation term operators we develop the first discretizations for compressible computational fluid dynamics that are primary conservative locally entropy stable in the fully discrete sense under a usual cfl condition explicit except for the parallelizable solution of a single scalar equation per element and arbitrarily high order accurate in space and time we demonstrate the accuracy and the robustness of the fully discrete explicit locally entropy stable solver for a set of test cases of increasing complexity

the tambara structure of the trace ideal for cyclic extensions abstract this paper explores the tambara functor structure of the trace ideal of a galois extension in the case of a pro cyclic extension we are able to explicitly determine the generators of the ideal furthermore we show that the absolute trace ideal of a cyclic group is strongly principal when viewed as an ideal of the burnside tambara functor applying our results we calculate the trace ideal for extensions of finite fields the appendix determines a formula for the norm of a quadratic form over an arbitrary finite extension of a finite field

numerical analysis of coupled systems of nonlinear parabolic equations this paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method three monotone iteration processes for the finite difference system are presented and the sequences of iterations are shown to converge monotonically to a unique solution of the system including an existence uniqueness comparison theorem a theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary value problem an application to a reaction diffusion model in chemical engineering and combustion theory is given

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12