existence and blow up for a degenerate parabolic equation with nonlocal source in this paper we investigate the positive solution of nonlinear degenerate equation ut up u au uq dx with dirichlet boundary condition conditions on the existence of global and blow up solution are given furthermore it is proved that there exist two positive constants c1 c2 such that c1 t t 1 p q maxx u x t c2 t t 1 p q

blow up and global existence for a nonlocal degenerate parabolic system abstract this paper investigates the blow up and global existence of nonnegative solutions of the system u t u m a v p v t v n b u q x t 0 t with homogeneous dirichlet boundary data where r n is a bounded domain with smooth boundary m n 1 1 p q a b 0 and dx it is proved that if pq mn there exist both global and blow up nonnegative solutions when pq mn we show that if the domain is sufficiently small every nonnegative solution is global while if the domain is large enough that is if it contains a sufficiently large ball there exists no global solution in particular when p n q m we show that every positive solution exists globally iff x dx 1 ab where x is the unique positive solution of the linear elliptic problem x 1 x x 0 x

on the uniqueness and ordering of steady states of predator prey systems this paper discusses the relationship between the uniqueness and the ordering of strictly positive solutions of elliptic predator prey interacting systems if v and u v are two such solutions with u or v v then u v v when the positive solutions are numerically close to the extreme case the solution is unique

facets for node packing the node packing problem is an extremely important problem given that it comprises the underlying structure of numerous optimization problems either directly or indirectly this paper presents a constraint approach which produces new facets for the node packing problem a number of different problem applications are solved incorporating this new constraint approach using a commercial software package on a personal computer demonstrating the effectiveness of the underlying facets in practice the new facet structures provide a means for addressing general dispersion and separation requirements using mathematical programming

some supercongruences occurring in truncated hypergeometric series abstract for the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p adic gamma functions that are stronger than those one can expect to prove using commutative formal group laws we prove a number of such supercongruences by using classical hypergeometric transformation formulae these formulae most of which are decades or centuries old allow us to write the terminating series as the ratio of products of values at this point sums have become quotients writing these quotients as p quotients we are in a situation that is well suited for proving p adic congruences these p functions can be p adically approximated by their taylor series expansions sometimes there is cancellation of the lower order terms leading to stronger congruences using this technique we prove among other things a conjecture of kibelbek and a strengthened version of a conjecture of van hamme

a quasilinear parabolic system arising in modelling of catalytic reactors a system of four quasilinear parabolic equations arising in modelling of catalytic reactors is studied the system is coupled in a nonstandard way we prove that the system has unique global solution the asymptotic behavior as t is studied

diffusive logistic equations with indefinite weights population models in disrupted environments the dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form u t d u m x cu u in 0 where u represents the population density c d 0 are constants describing the limiting effects of crowding and the diffusion rate of the population respectively and m x describes the local growth rate of the population if the environment is bounded and is surrounded by uninhabitable regions then u 0 on 0 the growth rate m x is positive on favourablehabitats and negative on unfavourable ones the object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled the models are shown to possess a unique stable positive steady state implying persistence for the population provided l d where is the principle positive eigenvalue for the problem m x in 0 on analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat in the limit as the diffusion rate d 0 the solutions tend toward the positive part of m x c and if m is discontinuous develop interior transition layers the analysis uses bifurcation and continuation methods the variational characterisation of eigenvalues upper and lower solution techniques and singular perturbation theory

some existence and nonexistence theorems for solutions of degenerate parabolic equations abstract the initial and boundary value problem for the degenerate parabolic equation v t v f v in the cylinder 0 r n bounded for a certain class of point functions satisfying v 0 e g v v m sign v is considered in the case that f v sign v c 1 v the equation has a global time solution the same is true for 1 provided the measure of is sufficiently small in the case that f v v is nondecreasing a condition is given on the initial state v x 0 which implies that the solution must blow up in finite time the existence of such initial states is discussed

asymptotic behavior of global solutions for a chemical reaction model this paper deals with a system of reaction diffusion equations modeling a chemical reaction process involving three substances the mathematical system consists of three semilinear partial differential equations of parabolic type with homogenous neumann boundary conditions the goal is to determine whether each substance has a positive asymptotic limit by the method of upper and lower solutions

finding a maximum clique in an arbitrary graph we describe a new type of branch and bound procedure for finding a maximum clique in an arbitrary graph g v e the two main ingredients both of o v e time complexity are i an algorithm for finding a maximal triangulated induced subgraph of g and ii an algorithm for finding a maximal k chromatic induced subgraph of g we discuss computational experience on randomly generated graphs with up to 400 vertices and 30 000 edges

blow up for a porous medium equation with a localized source in this paper we investigate the blow up properties of the positive solutions to a localized porous medium equation v t dv m av p 1v q 1 x 0 t subject to homogeneous dirichlet condition and positive initial datum v 0 x under appropriate hypotheses we establish the local existence and obtain that in the case of p 1 q 1m the solution of the above problem blows up for large initial datum while it admits a global solution for small initial datum moreover for the special case p 1 0 q 1 m and a is large under an additional hypothesis on the initial datum we can also obtain the asymptotic behavior of the blow up solution

total blow up versus single point blow up traditional thermal explosion theory is used to describe reaction initiation in condensed explosives and is limited formally to nondeformable materials kassoy and poland 4 significantly extended this theory to develop an ignition model for a reactive gas in a bounded container in order to describe the induction period during this induction period there is a spatially homogeneous pressure rise in the system which causes a com pressive heating effect in the constant volume container mathematically this compressibility of the gas is expressed by means of an integral term in the induction model for the temperature perturbation 0 x t this model is given by e ak 1 j e x t dx y x 2 0 x 0 d x 2 0

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

persistence in a periodic competitor competitor mutualist diffusion system in this paper we investigate the existence and the asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a competitor competitor mutualist model under dirichlet boundary conditions we shall prove that under certain conditions this system is persistent and under some other conditions it exhibits extinction or more exactly the species of mutualist extincts

an analysis of network location problems with distance constraints this paper concerns a class of network location problems with minimum or maximum separation requirements between uncapacitated facilities or between demand points and the facilities or both its purpose is three fold first it is to recognize distance constraints as increasing real life restrictions through various motivating illustrations using a new classification scheme the paper introduces a variety of distance constrained problems defined in a unified manner these include a number of new problems second it is to survey existing solution techniques available only for a few of such constrained problems finally it is to shed some light on yet unstudied problems by exploring possible extensions of some of the known solution techniques or discussing varying degrees of difficulties involved in particular the paper presents integer programming formulations of several new problems along with the results of applying linear programming relaxation methods although the computational experience is somewhat disappointing for some of these problems the results provide greater insight into the problems with the stated purpose it is hoped that this paper will stimulate future research in this important problem area

on a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium the main result of the paper is the uniqueness of nonnegative solutions of the cauchy problem and of the first and mixed boundary value problems for a class of degenerate parabolic equations which includes the model equation ut um xx un x where m 1 and n 0 in particular n is allowed to be smaller than one the proof is based on a refined test function argument the condition that u be nonnegative is crucial but the restriction to one space variable is not

divisibility results concerning truncated hypergeometric series abstract in this paper using the well known karlsson minton formula we mainly establish two divisibility results concerning truncated hypergeometric series let n 2 and q 0 be integers with 2 n or 2 q we show that k 0 p 1 q p n k n 1 k n 0 mod p 3 and p n k 0 p 1 1 k n p n q 2 k n 0 mod p 3 for any prime p max n q 1 n 1 where x k denotes the pochhammer symbol defined by x k 1 k 0 x x 1 x k 1 k 0 let n 4 be an even integer then for any prime p with p 1 mod n the first congruence above implies that k 0 p 1 1 n k n 1 k n 0 mod p 3 this confirms a recent conjecture of guo

factors of some truncated basic hypergeometric series abstract we prove that certain basic hypergeometric series truncated at k n 1 have the factor n q 2 where n q is the n th cyclotomic polynomial this confirms two recent conjectures of the author and zudilin we also put forward some conjectures on q congruences modulo n q 2

uniform blow up rate for diffusion equations with localized nonlinear source abstract in this short paper we investigate blow up rate of solutions of reaction diffusion equations with localized reactions we prove that the solutions have a global blow up and the rate of blow up is uniform in all compact subsets of the domain

critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources this paper deals with two classes of parabolic systems with localized nonlinear sources the critical exponents as well as the estimates for blow up rates and boundary layer profiles are determined

global existence and finite time blow up for a degenerate reaction diffusion system abstract this paper investigates the blow up and global existence of solutions of the degenerate reaction diffusion system u t u m u v p v t v n u q v x t 0 t with homogeneous dirichlet boundary data where r n is a bounded domain with smooth boundary m n 1 0 and p q 0 it is proved that if m n and pq m n every nonnegative solution is global whereas if m or n or pq m n there exist both global and blow up nonnegative solutions when m n and pq m n we show that there exists 1 which depends on the parameters p q m n such that all positive solutions are global if 1 while if 1 1 all positive solutions blow up in finite time where 1 is the first dirichlet eigenvalue for the laplacian on

boundedness and blowup for nonlinear degenerate parabolic equations the author deals with the quasilinear parabolic equation ut u fi g u u bu fi 1 f u ru with dirichlet boundary conditions in a bounded domain where f and g are lower order terms he shows that under suitable conditions on f and g whether the solution is bounded or blows up in a flnite time depends only on the flrst eigenvalue of i in with dirichlet boundary condition for some special cases the result is sharp

blow up properties for a degenerate parabolic system with nonlinear localized sources abstract this paper deals with blow up properties for a degenerate parabolic system with nonlinear localized sources subject to the homogeneous dirichlet boundary conditions the main aim of this paper is to study the blow up rate estimate and the uniform blow up profile of the blow up solution our conclusions extend the results of l l du blow up for a degenerate reaction diffusion system with nonlinear localized sources j math anal appl 324 2006 304 320 at the end the blow up set and blow up rate with respect to the radial variable is considered when the domain is a ball

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

on nonlinear coupled reaction diffusion equations this paper is concerned with the existence and uniqueness of solutions of reaction diffusion equations arising in many applications and often coupled our approach to the problem is based on converting the coupled equations into a system of volterra fredholm type integral equations by means of the green s function representation and using the banach fixed point theorem an application to nonlinear second order evolution equations is also indicated

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

the asymptotic behavior of blowup solution of localized nonlinear equation abstract in this paper we are concerned with the growth rate of blowup solution to the equation formula using self similar solution technique and comparison method we obtain the growth rate of blowup solution and observe that the boundary layer phenomena occurs

a reaction diffusion system of a competitor competitor mutualist model we investigate the homogeneous dirichlet problem and neumann problem to a reactiondiffusion system of a competitor competitor mutualist model the existence uniqueness and boundedness of the solutions are established by means of the comparison principle and the monotonicity method for the dirichlet problem we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities for the neumann problem we analyze the contant equilibrium solutions and their stabilities the main method used in studying of the stabilities is the spectral analysis to the linearized operators the o d e problem to the same model was proposed and studied by b rai h i freedman and j f addicott

total versus single point blow up of solutions of a semilinear parabolic equation with localized reaction abstract in this paper we study the initial boundary value problem of a semilinear parabolic equation with localized reaction p u t u u p u q x t x t b 0 t u x t 0 x t b 0 t u x 0 u 0 x x b where b is a unit ball in r n x b and p q 0 for the case x 0 we completely classify blow up solutions of p into total blow up cases and single point blow up cases according to the values p and q moreover we give the blow up rates of solutions near the blow up time for the other case x 0 we show total blow up and single point blow up of solutions of p in some cases depending on p and q

coupled diffusion systems with localized nonlinear reactions this paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit ui upii 1 x0 t i 1 k uk 1 u1 in 0 t with boundary conditions ui 0 on 0 t we show that the solution has a global blowup the exact rate of the blowup is obtained and we also derive the estimate of the boundary layer and on the asymptotic behavior of the solution in the boundary layer

turbulent transport and the random occurrence of coherent events abstract we suggest that the transport properties and dissipation rates of a wide class of turbulent flows are determined by the random occurrence of coherent events which correspond to certain orbits which we call homoclinic excursions in the high dimensional strange attractor homoclinic excursions are trajectories in the noncompact phase space that are attracted to special orbits which connect saddle points in the finite region of phase space to infinity and represent organized structures in the flow field this picture also suggests that one can compute fluxes using a relatively low dimensional description of the flow a method for extracting the organized structures from a time series is given and provides a local analogue of the notion of lyapunov exponents

uniform blow up profile for a degenerate parabolic system with nonlocal source in this paper we establish the local existence of the solution and the finite time blow up result for the following system ut ur1 u a updx forx ohm t 0 ut ur2 u b uqdx forx ohm t 0 where p q 1 and 0 r1 r2 1 moreover it is proved that the solution has global blow up and limt t t t p 1 r2 yu x t 1 r1 11 r1 a a y p 1 r2 y q 1 r1 py xa p 1 r2 b1 r2 y limt t t t q 1 r1 yu x t 1 r2 11 r2 b a y q 1 r1 y p 1 r2 qy xb q 1 r1 a1 r1 y uniformly on compact subsets of where pq 1 r1 1 r2 and t is the blow up time

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

blow up for a degenerate reaction diffusion system with nonlinear localized sources abstract this paper deals with the global existence and blow up of nonnegative solution of the degenerate reaction diffusion system with nonlinear localized sources involved a product with local terms we investigate the influence of localized sources and local terms on global existence and blow up for this system moreover we establish the precise blow up estimates finally for the special case p 1 p 2 0 we show the blow up set is whole region and the uniform blow up profiles are obtained these extend a resent work of chen and xie in y chen c xie blow up for a porous medium equation with a localized source appl math comput 159 2004 79 93 which considered the single equation with localized sources

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

symbolic summation methods and hypergeometric supercongruences abstract in this paper via the wz method and the summation package sigma we establish the following two supercongruences k 0 p 1 2 3 k 1 1 2 k 2 1 2 k 4 k k 3 p 6 p 3 1 p 2 p 3 1 p e p 3 mod p 4 k 0 p 1 3 k 1 1 2 k 2 1 2 k 4 k k 3 p 2 p 3 mod p 4 where p 3 is a prime e p 3 is the p 3 th euler number and 1 p 1 p 1 2 is the legendre symbol the first congruence modulo p 3 confirms a recent conjecture of guo and schlosser

weak solution of the equation for a fractional porous medium with a forcing term we consider the cauchy problem with a forcing term for a fractional porous medium which arises in statistical mechanics and heat control the existence and uniqueness of a weak energy solution are established using implicit time discretization and l 1 contraction semigroup arguments

a reaction diffusion system with mixed type coupling this paper deals with asymptotic behavior of solutions to a reaction diffusion system coupled via localized and local sources u t du v p x t t v t dv u q both the initial boundary problem with null dirichlet boundary condition and the cauchy problem are considered to study the interaction between the two kinds of sources for the initial boundary problem we prove that the nonglobal solutions blow up everywhere in the bounded domain with uniform blow up profiles in addition it is interesting to observe that the cauchy problem admits an infinity fujita exponent namely the solutions blow up under any nontrivial and nonnegative initial data whenever pq 1 all these imply that the blow up behavior of solutions is governed by the localized source for the two problems with mixed type coupling

on van hamme s a 2 and h 2 supercongruences abstract in 1997 van hamme conjectured 13 ramanujan type supercongruences labeled a 2 m 2 using some combinatorial identities discovered by sigma we extend a 2 and h 2 to supercongruences modulo p 4 for primes p 3 mod 4 which appear to be new

global existence and blow up for a porous medium system with nonlocal boundary conditions and nonlocal sources abstract this paper is devoted to a porous medium system subject to nonlocal boundary conditions and with nonlocal sources we investigate the global existence and blow up in finite time of a nonnegative solution by using a sub super solution method moreover under appropriate hypotheses for the conditions we obtain asymptotic properties of the solutions

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

the blowup property of solutions to some diffusion equations with localized nonlinear reactions abstract in this paper we investigate the blowup property of solutions to the equation u t u u x 0 t where x0 is a fixed point in the domain we show that under certain conditions the solution blows up in finite time moreover we prove that the set of all blowup points is the whole region furthermore the growth rate of solutions near the blowup time is also derived finally the results are generalized to the following nonlocal reaction diffusion equation u t u u dx

harvest scheduling subject to maximum area restrictions exploring exact approaches we consider a spatial problem arising in forest harvesting for regulatory reasons blocks harvested should not exceed a certain total area typically 49 hectares traditionally this problem called the adjacency problem has been approached by forming a priori blocks from basic cells of 5 to 25 hectares and solving the resulting mixed integer program superior solutions can be obtained by including the construction of blocks in the decision process the resulting problem is far more complex combinatorially we present an exact algorithmic approach that has yielded good results in computational tests this solution approach is based on determining a strong formulation of the linear programming problem through a clique representation of a projected problem

a q microscope for supercongruences abstract by examining asymptotic behavior of certain infinite basic q hypergeometric sums at roots of unity that is at a q microscopic level we prove polynomial congruences for their truncations the latter reduce to non trivial super congruences for truncated ordinary hypergeometric sums which have been observed numerically and proven rarely a typical example includes derivation from a q analogue of ramanujan s formula n 0 4 n 2 n 2 n n 2 2 8 n 3 2 n 8 n 1 2 3 of the two supercongruences s p 1 p 3 p mod p 3 and s p 1 2 p 3 p mod p 3 valid for all primes p 3 where s n denotes the truncation of the infinite sum at the n th place and 3 stands for the quadratic character modulo 3

asymptotic analysis to a parabolic equation with a weighted localized source abstract this paper deals with a nonlinear parabolic equation with a more complicated source term which is a product of localized source u q 0 t local source u p x t and weight function a x we investigate how the three factors influence the asymptotic behavior of solutions it is shown that the blow up set consists of single point x 0 if p 1 when 0 p 1 with p q 1 the blow up take place everywhere in b moreover the blow up rate estimate is established with more precise coefficients determined

global bifurcation of positive radial solutions for an elliptic system in reactor dynamics in this paper we are concerned with the existence of positive radial solutions of the elliptic system email protected email protected f x u r 1 0 is a constant m 0 is a parameter and 0 0 is continuous and f t s 0 for all t s r 1 r 2 x 0 under some appropriate conditions on the nonlinearity f we show that the above system possesses at least one positive radial solution for any email protected 0 the proof of our main results is based upon bifurcation techniques

boundedness of global solutions for a nonlinear degenerate parabolic porous medium system with localized sources abstract this paper deals with nonlinear degenerate parabolic porous medium system with localized sources it is shown that under certain conditions solutions of the equation blow up in finite time for large a and b or large initial data while there exist global positive solutions for small a and b or small initial data moreover it is also shown that all global positive solutions of the above equation are uniformly bounded these extend a recent work of chen et al in y chen q liu h gao boundedness of global solutions of a porous medium equation with a localized source nonlinear anal 64 2006 2168 2182 which considered the single equation with localized source

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

blow up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition this paper is devoted to a nonlinear parabolic equation subject to nonlocal boundary condition and with nonlocal reaction source some criteria on this problem which determine whether the solutions blow up in a finite time or exist globally are given moreover the blow up rate estimates are also obtained

blow up properties for a degenerate parabolic system with nonlinear localized sources in this paper we investigate the initial boundary problem of a degenerate parabolic system with nonlinear localized sources we classify the blow up solutions into global blow up cases and single point blow up cases according to the values of m n p i q i furthermore we obtain the uniform blow up profiles of solutions for the global blow up case finally we give some numerical examples to verify the results these extend and generalize a recent work of one of the authors l du blow up for a degenerate reaction diffusion systems with nonlinear localized sources j math anal appl 324 2006 304 320 which only considered uniform blow up profiles under the special case p 1 p 2 0

periodic solutions of coupled semilinear parabolic boundary value problems the study of periodic solutions to parabolic differential systems goes back to j fourier who investigated the linear heat equation for the determination of temperature oscillation on earth cf 141 in recent years attention has been given to nonlinear parabolic boundary value problems cf l 2 4 6 7 15 16 however most of the discussions in the literature are concerned with a single parabolic equation under dirichlet type boundary condition due to the recent development in the biochemical and biological fields there arise various types of reactiondiffusion systems e g see lo 121 an interesting problem in some of these systems such as the belousov zhabotinskii reaction model is an understanding of the oscillating nature of the solution in this paper we investigate periodic solutions for a coupled system of parabolic boundary value problems in a one dimensional domain under various boundary conditions specifically the equations under consideration are given by