weak solutions of the shigesada kawasaki teramoto equations and their attractors abstract we derive the global existence of weak solutions of the shigesada kawasaki teramoto systems in any space dimension d 1 with a rather general condition on the coefficients the existence is established using finite differences in time with truncations and an argument of stampacchia s maximum principle to show the positivity of the solutions we derive also the existence of a weak global attractor

an extension of kesten s criterion for amenability to topological markov chains abstract the main results of this note extend a theorem of kesten for symmetric random walks on discrete groups to group extensions of topological markov chains in contrast to the result in probability theory there is a notable asymmetry in the assumptions on the base that is it turns out that under very mild assumptions on the continuity and symmetry of the associated potential amenability of the group implies that the gurevic pressures of the extension and the base coincide whereas the converse holds true if the potential is holder continuous and the topological markov chain has big images and preimages finally an application to periodic hyperbolic manifolds is given

geometric exponents and kleinian groups suppose lambda is the limit set of an analytically finite kleinian group and that omega j is an enumeration of the components of omega s 2 setminus lambda then sum j diam omega j 2 infty this had been conjectured by maskit we also define a number of different geometric critical exponents associated to a compact set in the plane which generalize the index of besicovitch and taylor on the line although these exponents may differ for general sets we show that they are all equal when lambda is the limit set of a non elementary analytically finite kleinian group and they agree with the classical poincare exponent

global existence of solutions to a cross diffusion predator prey system with holling type ii functional response this paper is concerned with a cross diffusion system arising in a predator prey population model with holling type ii functional response in a bounded domain with no flux boundary condition employing the energy estimates and gagliardo nirenberg type inequalities to establish w 2 1 bounds uniform in time the global existence and uniform boundedness of solutions for a cross diffusion system are proved the global asymptotic stability of the constant positive steady state is also investigated

function theory random paths and covering spaces pour des varietes de riemann connexes m on etudie la relation entre la theorie de fonction harmonique sur m les proprietes statistiques des chemins aleatoires sur m et la structure geometrique globale de m

discrete groups and holomorphic functions we determine conditions under which the quotient of a kahler hadamard manifold by a torsion free discrete group of isometries admits a big set of nontrivial holomorphic functions we also generalize a theorem of g a margulis on centerless of cocompact discrete groups of automorphisms of a caratheodory hyperbolic manifold by a different approach based on the caratheodory pseudodistance

analytic continuation of the resolvent of the laplacian on symmetric spaces of noncompact type let m g be a globally symmetric space of noncompact type of arbitrary rank and its laplacian we introduce a new method to analyze and the resolvent 1 this has origins in quantum n body scattering but is independent of the classical theory of spherical functions and is analytically much more robust we expect that suitably modified it will generalize to locally symmetric spaces of arbitrary rank as an illustration of this method we prove the existence of a meromorphic continuation of the resolvent across the continuous spectrum to a riemann surface multiply covering the plane we also show how this continuation may be deduced using the theory of spherical functions in summary this paper establishes a long suspected connection between the analysis on symmetric spaces and n body scattering

coexistence theorem of steady states for nonlinear self cross diffusion systems with competitive dynamics in this paper we discuss the existence of positive solutions to certain nonlinear elliptic systems representing competitive interaction with self cross diffusions between two species the method employed is the fixed point index theory in a positive cone sufficient conditions for the existence of positive solutions are provided

smooth solutions to a quasi linear system of diffusion equations for a certain population model abstract the system of diffusion equations proposed by kawasaki shigesada and teramoto describes a population model of two competing species with self and cross population pressures the densities of the two species are denoted by u and v in this paper the author studies the initial boundary value problem associated with the neumann boundary condition corresponds to the case where the flux is zero at the boundary many investigators have considered nonlinear diffusion systems arising from various physical and biological problems these equations however have a special structure the highest order derivatives are not coupled or at least the coefficient matrix for the highest order derivatives is positive definite this is not the case for the system and hence some of the techniques which are effective for the system are no longer applicable to our case nevertheless we can still use sobolevski s method see reference 2 to establish the local existence of solutions under the special assumption c1 c2 in we can also prove the global existence of solutions by energy estimates the unusual structure of seems to make it difficult to settle the question of asymptotic stability of solutions

error estimates for discrete time approximations of nonlinear cross diffusion systems this paper is concerned with nonlinear and linear discrete time algorithms for cross diffusion systems the nonlinear scheme corresponds to backward differences in time and the linear algorithm is a very easy to implement scheme proposed by the author esaim math model numer anal 45 2011 pp 1141 1161 the main purpose of this paper is to derive convergence rates of the discrete time schemes we obtain the same orders for both the nonlinear and the linear scheme moreover these orders are optimal we also establish uniqueness and regularity results of weak solutions of the cross diffusion systems

on a cross diffusion population model deduced from mutation and splitting of a single species we deduce a particular case of the population cross diffusion model introduced by shigesada et al 1979 1 by using the ideas of mutation and splitting from a single species as described by sanchez palencia for ode s systems sanchez palencia 2011 21 the resulting equations of the pde system only differ in the cross diffusion terms the corresponding diffusion matrix being self diffusion dominated which implies that the well known population segregation patterns of the shigesada et al model do not appear in this case we prove existence and uniqueness of solutions of the pde system and use a finite element approximation to discuss numerically stability properties of solutions with respect to the parameters in comparison with related models

uniform boundedness and convergence of solutions to cross diffusion systems abstract uniform boundedness and convergence of global solutions are proved for cross diffusion systems in population dynamics gagliardo nirenberg type inequalities are used in the estimates of solutions in order to establish w 2 1 bounds uniform in time in each step of estimates the contribution of the diffusion coefficients are emphasized and it is concluded that the uniform bound remains independent of the growth of the diffusion coefficient in the system hence convergence of solutions are established for systems with large diffusion coefficients

on the critical exponent of infinitely generated veech groups we prove the existence of veech groups having a critical exponent strictly greater than any elementary fuchsian group i e frac 1 2 but strictly smaller than any lattice i e 1 more precisely every affine covering y of a primitive l shaped veech surface x ramified over the singularity and a non periodic connection point p in x has such a veech group mathrm sl y hubert and schmidt duke math j 123 49 69 2004 showed that these veech groups are infinitely generated and of the first kind we use a result of roblin and tapie monogr enseign math 43 61 92 2013 which connects the critical exponent of mathrm sl y with the cheeger constant of the schreier graph of mathrm sl x mathrm stab mathrm sl x p the main task is to show that the cheeger constant is strictly positive i e the graph is non amenable in this context we introduce a measure of the complexity of connection points that helps to simplify the graph to a forest for which non amenability can be seen easily

modeling spatial adaptation of populations by a time non local convection cross diffusion evolution problem abstract in 19 sighesada et al presented a system of partial differential equations for modeling spatial segregation of interacting species apart from competitive lotka volterra reaction and population pressure cross diffusion terms a convective term modeling the populations attraction to more favorable environmental regions is included in this article we introduce a modification of their convective term to take account for the notion of spatial adaptation of populations after describing the model we briefly discuss its well possedness and propose a numerical discretization in terms of a mass preserving time semi implicit finite differences scheme finally we provide the results of two biologically inspired numerical experiments showing qualitative differences between the original model of 19 and the model proposed in this article

coexistence of a general elliptic system in population dynamics this paper is concerned with a strongly coupled elliptic system representing a competitiveinteraction between two species we give a sufficient condition for the existence of positive solutions an example is also given to show that there is a coexistence of a steady state if the cross diffusions or the intraspecific competitions are weak

cogrowth and amenability of discrete groups abstract let g be a group and g1 gt a set of generators there are approximately 2t 1 n reduced words in g1 gt of length n let gg n be the number of those which represent 1g we show that lim n gg n 1 n exists clearly 1 2t 1 log log 2t 1 is the cogrowth 0 1 in fact 0 1 2 1 the entropic dimension of g is shown to be 1 it is then proved that d g 1 if and only if g is free on g1 gt and d g 0 if and only if g is amenable

amenable covers for surfaces and growth of closed geodesics abstract in this article we show that the rate of growth of closed geodesics up to translation on an amenable cover of a compact surface is the same as that on the underlying space this generalizes the result for negatively curved surfaces

uniform boundedness and convergence of solutions to the systems with a single nonzero cross diffusion uniform boundedness and convergence of global solutions are proved for quasilinear parabolic systems with a single nonzero cross diffusion in population dynamics gagliardo nirenberg type inequalities are used in the estimates of solutions in order to establish w12 bounds uniform in time by using the uniform bound convergence of solutions are established for systems with large diffusion coefficients in the weak competition case

complete manifolds with positive spectrum ii in this paper we continued our investigation of complete manifolds whose spectrum of the laplacian has an optimal positive lower bound in particular we proved a splitting type theorem for n dimensional manifolds that have a finite volume end this can be viewed as a study of the equality case of a theorem of cheng

on the bottom of spectra under coverings for a riemannian covering m 1 rightarrow m 0 of connected riemannian manifolds with respective fundamental groups gamma 1 subseteq gamma 0 we show that the bottoms of the spectra of m 0 and m 1 coincide if the right action of gamma 0 on gamma 1 backslash gamma 0 is amenable

lyapunov spectra for kms states on cuntz krieger algebras we study relations between h kms states on cuntz krieger algebras and the dual of the perron frobenius operator mathcal l beta h ast generalising the well studied purely hyperbolic situation we obtain under mild conditions that for an expansive dynamical system there is a one one correspondence between h kms states and eigenmeasures of mathcal l beta h ast for the eigenvalue 1 we then apply these general results to study multifractal decompositions of limit sets of essentially free kleinian groups g which may have parabolic elements we show that for the cuntz krieger algebra arising from g there exists an analytic family of kms states induced by the lyapunov spectrum of the analogue of the bowen series map associated with g furthermore we obtain a formula for the hausdorff dimensions of the restrictions of these kms states to the set of continuous functions on the limit set of g if g has no parabolic elements then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with g

martin boundaries of elliptic skew products semismall perturbations and fundamental solutions of parabolic equations abstract we consider positive solutions of elliptic partial differential equations on non compact domains of riemannian manifolds we explicitly determine martin boundaries and martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short long time estimates for fundamental solutions of parabolic equations

large time behavior of the heat kernel and the behavior of the green function near criticality for nonsymmetric elliptic operators abstract let p be a second order elliptic operator which is defined on a domain r n and let w x be a nonzero nonnegative function assume that p p w x admits a positive minimal green function g p x y for all lim 0 g p x y f x y where f 0 for x y unless p and p admit ground states x and x respectively with eigenvalue zero such that z w z z dz in this case f x y x y z w z z dx moreover if z z dz then the heat kernel k x y t of the parabolic equation lu u t pu 0 satisfies lim t k x y t x y z z dz

hausdorff dimension and conformal dynamics iii computation of dimension this paper presents an eigenvalue algorithm for accurately computing the hausdorff dimension of limit sets of kleinian groups and julia sets of rational maps the algorithm is applied to schottky groups quadratic polynomials and blaschke products yielding both numerical and theoretical results dimension graphs are presented for a the family of fuchsian groups generated by reflections in 3 symmetric geodesics b the family of polynomials f c z z 2 c c 1 1 2 and c the family of rational maps f t z z t 1 z t 0 1 we also calculate h dim 1 305688 for the apollonian gasket and h dim j f 1 3934 for douady s rabbit where f z z 2 c satisfies f 3 0 0

amenability critical exponents of subgroups and growth of closed geodesics let gamma be a non elementary convex co compact group of isometries of a pinched hadamard manifold x we show that a normal subgroup gamma 0 has critical exponent equal to the critical exponent of gamma if and only if gamma gamma 0 is amenable we prove a similar result for the exponential growth rate of closed geodesics on x gamma these statements are analogues of classical results of kesten for random walks on groups and brooks for the spectrum of the laplacian on covers of riemannian manifolds

global existence analysis of cross diffusion population systems for multiple species the existence of global in time weak solutions to reaction cross diffusion systems for an arbitrary number of competing population species is proved the equations can be derived from an on lattice random walk model with general transition rates in the case of linear transition rates it extends the two species population model of shigesada kawasaki and teramoto the equations are considered in a bounded domain with homogeneous neumann boundary conditions the existence proof is based on a refined entropy method and a new approximation scheme global existence follows under a detailed balance or weak cross diffusion condition the detailed balance condition is related to the symmetry of the mobility matrix which mirrors onsager s principle in thermodynamics under detailed balance and without reaction the entropy is nonincreasing in time but counter examples show that the entropy may increase initially if detailed balance does not hold

positive steady states for a prey predator model with some nonlinear diffusion terms abstract this paper discusses a prey predator system with strongly coupled nonlinear diffusion terms we give a sufficient condition for the existence of positive steady state solutions our proof is based on the bifurcation theory some a priori estimates for steady state solutions will play an important role in the proof

orbit counting for some discrete groups acting on simply connected manifolds with negative curvature in this article we develop a method of deriving asymptotic formulae for the orbital counting function for the action of certain discrete groups of isometries of simply connected negatively curved manifolds we consider the particular case of normal subgroups 0 of a co compact group 0 for which the quotient 0 k even in the special case of manifolds ofconstant negative curvature this leads to new results in particular we have asymptotic estimates for some groups which arenot geometrically finite

uniform boundedness and convergence of global solutions to a strongly coupled parabolic system with three competitive species uniform boundedness and convergence of global solutions are proved for strongly coupled parabolic systems with cross diffusions dominated by self diffusions in population dynamics gagliardo nirenberg inequalities are used in the estimates of solutions in order to establish w 2 1 bounds uniform in time

rigidity of amalgamated product in negative curvature let gamma be the fundamental group of a compact n dimensional riemannian manifold x of sectional curvature bounded above by 1 we suppose that gamma is a free product of its subgroup a and b over the amalgamated subgroup c we prove that the critical exponent delta c of c satisfies delta c geq n 2 the equality happens if and only if there exist an embedded compact hypersurface y in x totally geodesic of constant sectional curvature 1 with fundamental group c and which separates x in two connected components whose fundamental groups are a and b similar results hold if gamma is an hnn extension or more generally if gamma acts on a simplicial tree without fixed point

pathwise mild solutions for quasilinear stochastic partial differential equations abstract stochastic partial differential equations spdes have become a key modeling tool in applications yet there are many classes of spdes where the existence and regularity theory for solutions is not completely developed here we contribute to this aspect and prove the existence of mild solutions for a broad class of quasilinear cauchy problems including among others cross diffusion systems as a key application our solutions are local in time and are derived via a fixed point argument in suitable function spaces the key idea is to combine in a suitable way the classical theory of deterministic quasilinear parabolic partial differential equations pdes with recent theory of evolution semigroups we also show how to apply our theory to the shigesada kawasaki teramoto skt model furthermore we provide examples of blow up and ill posed operators which can occur after finite time showing that solutions can only be local in time for general quasilinear spdes while they might be global in time for special subclasses of problems

optimal design of non minimum phase control systems with large plant uncertainty abstract a given linear time invariant controlled plant with non minimum phase and or unstable transfer function is considered that has significant plant parameter uncertainty but the ranges of the uncertain parameters are known it is desired that in response to a deterministic input over the entire range of parameter uncertainty the system output should lie with specified bounds a practical optimal design procedure that has been presented in the authors previous work is extended to deal with this problem furthermore the design philosophy is modified so that the two degree of freedom system configuration can be simplified

coexistence of three species in a strongly coupled elliptic system abstract a strongly coupled elliptic system which describes three interacting species with homogeneous dirichlet boundary conditions is considered it is shown that there is no coexistence state if diffusion rates are strong or if the intrinsic growth rates are slow making use of the schauder fixed point theory we derive some sufficient conditions to have a semi coexistence or a coexistence state for the strongly coupled elliptic problem moreover our results reveal that this problem possesses at least one coexistence state if cross diffusions and intra specific competitions are weak

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

critical exponents of normal subgroups the spectrum of group extended transfer operators and kazhdan distance abstract for a pinched hadamard manifold x and a discrete group of isometries of x the critical exponent is the exponential growth rate of the orbit of a point in x under the action of we show that the critical exponent for any family n of normal subgroups of 0 has the same coarse behaviour as the kazhdan distances for the right regular representations of the quotients 0 the key tool is to analyse the spectrum of transfer operators associated to subshifts of finite type for which we obtain a result of independent interest

on almost fuchsian manifolds almost fuchsian manifold is a class of complete hyperbolic threemanifolds a such three manifold is a quasi fuchsian manifold that contains a closed incompressible minimal surface with principal curvatures everywhere in the range of 1 1 in such a manifold the minimal surface is unique and embedded hence one can parametrize these hyperbolic three manifolds by their minimal surfaces in this paper we obtain estimates on several geometric and analytical quantities of an almost fuchsian manifold m in terms of the data on the minimal surface in particular we obtain an upper bound for the hyperbolic volume of the convex core of m and an upper bound on the hausdorff dimension of the limit set associated to m we also constructed a quasi fuchsian manifold which admits more than one minimal surface and it does not admit a foliation of closed surfaces of constant mean curvature

length distortion and the hausdorff dimension of limit sets let be a convex co compact quasi fuchsian kleinian group we define the distortion function along geodesic rays lying on the boundary of the convex hull of the limit set where each ray is pointing in a randomly chosen direction the distortion function measures the ratio of the intrinsic to extrinsic metrics and is defined asymptotically as the length of the ray goes to infinity our main result is that the distortion function is both almost everywhere constant and bounded above by the hausdorff dimension of the limit set of as a consequence we are able to provide a geometric proof of the following result of bowen if the limit set of is not a round circle then the hausdorff dimension of the limit set is strictly greater than one the proofs are developed from results in patterson sullivan theory and ergodic theory

bounds for eigenfunctions of the laplacian on noncompact riemannian manifolds we deal with eigenvalue problems for the laplacian on noncompact riemannian manifolds m of finite volume sharp conditions ensuring l q m and l infinity m bounds for eigenfunctions are exhibited

recurrence and transience of branching diffusion processes on riemannian manifolds we relate the recurrence and transience of a branching diffusion process on a riemannian manifold m to some properties of a linear elliptic operator onm including spectral properties there is a trade off between the tendency of the transient brownian motion to escape and the birth process of the new particles if the latter has a high enough intensity then it may override the transience of the brownian motion leading to the recurrence of the branching process and vice versa in the case of a spherically symmetric manifold the critical intensity of the population growth can be found explicitly

holder regularity for certain strongly coupled parabolic systems abstract we present a shorter proof to show holder continuity of bounded solutions to a general class of quasilinear parabolic equations the proof will be extended to obtain regularity results for bounded solutions to certain strongly coupled or cross diffusion quasilinear parabolic systems

new results for triangular reaction cross diffusion system abstract we present an approach based on entropy and duality methods for triangular reaction cross diffusion systems of two equations in which cross diffusion terms appear only in one of the equations thanks to this approach we recover and extend many existing results on the classical triangular shigesada kawasaki teramoto model

on global existence of solutions to a cross diffusion system abstract we consider a strongly coupled nonlinear parabolic system which arises in population dynamics in n dimensional domains n 1 we prove the global existence of classical solutions to the system for n 10

existence of stationary solutions with transition layers for a class of cross diffusion systems this paper is concerned with the existence of stationary solutions for some cross di usion systems with small parameters using a singular perturbation method we prove the existence of stationary solutions with boundary and interior layers which extends the results of fife and ito to the cross di usion cases

random dispersal versus fitness dependent dispersal abstract this work extends previous work cantrell et al 2008 9 on fitness dependent dispersal for a single species to a two species competition model both species have the same population dynamics but one species adopts a combination of random and fitness dependent dispersal and the other adopts random dispersal global existence of smooth solutions to the time dependent quasilinear parabolic system is studied when a single species has a strong tendency to move up its fitness gradient it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution cantrell et al 2008 9 for the two species competition model if one species has strong tendency to move up its fitness gradient such approximately ideal free dispersal is advantageous relative to random dispersal bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate

brief paper multivariable model reference linear quadratic optimal systems this paper deals with model reference linear quadratic optimal control design in the frequency domain for multiple input multiple output systems an explicit equation is given for the 1dof one degree of freedom controller which minimizes a given quadratic cost function some optimal systems are shown to be the special cases of this generalized result for the system with minimum phase zeros the equivalent 2dof two degrees of freedom control system is designed so that the loop transfer matrix can satisfy the return difference equality i e the system can recover the robustness properties as in time domain lqr optimal systems

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

escaping geodesics in riemannian surfaces with variable negative curvature abstract in this paper we give a lower bound for the visual hausdorff dimension of the geodesics escaping through different ends of riemannian surfaces with pinched negative curvature this allows to show that in any riemannian surface with pinched negative curvature and infinite area there is a large set of geodesics escaping to infinity

related aspects of positivity in riemannian geometry pour une variete de riemann on etudie le lien entre le point 0 du l 2 spectre le plus proche de zero pour l extension de friedrich d un operateur semi defini symetrique et le taux exponentiel de transition d un operateur de markoff conservant la positivite

ends of locally symmetric spaces with maximal bottom spectrum let x be a symmetric space of non compact type and gnx a locally sym metric space then the bottom spectrum l1 gnx satisfies the inequality l1 gnx e l1 x we show that if equality l1 gnx l1 x holds then gnx has either one end which is necessarily of infinite volume or two ends one of infinite volume and another of finite vol ume in the latter case gnx is isometric to r 1 n endowed with a multi warped metric where n is compact

hausdorff dimension and conformal dynamics i strong convergence of kleinian groups this paper investigates the behavior of the hausdorff dimensions of the limit sets n and of a sequence of kleinian groups n where m h is geometrically finite we show if n strongly then a mn h 3 n is geometrically finite for all n 0 b n in the hausdorff topology and c h dim n h dim if h dim 1 on the other hand we give examples showing the dimension can vary discontinuously under strong limits when h dim 1 continuity can be recovered by requiring that accidental parabolics converge radially similar results hold for higher dimensional manifolds applications are given to quasifuchsian groups and their limits

a sharp estimate for the bottom of the spectrum of the laplacian on kahler manifolds on a complete noncompact kahler manifold we prove that the bottom of the spectrum for the laplacian is bounded from above by m 2 if the ricci curvature is bounded from below by 2 m 1 then we show that if this upper bound is achieved then the manifold has at most two ends these results improve previous results on this subject proved by p li and j wang in l w3 and l w under assumptions on the bisectional curvature

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

coexistence and asymptotic periodicity in a competitor competitor mutualist model in this paper the competitor competitor mutualist three species lotka volterra model is discussed firstly by schauder fixed point theory the coexistence state of the strongly coupled system is given applying the method of upper and lower solutions and its associated monotone iterations the true solutions are constructed our results show that this system possesses at least one coexistence state if cross diffusions and cross reactions are weak secondly the existence and asymptotic behavior of t periodic solutions for the periodic reaction diffusion system under homogeneous dirichlet boundary conditions are investigated sufficient conditions which guarantee the existence of t periodic solution are also obtained

strongly coupled elliptic systems and applications to lotka volterra models with cross diffusion abstract the aim of this paper is to investigate the existence and method of construction of solutions for a general class of strongly coupled elliptic systems by the method of upper and lower solutions and its associated monotone iterations the existence problem is for nonquasimonotone functions arising in the system while the monotone iterations require some mixed monotone property of these functions applications are given to three lotka volterra model problems with cross diffusion and self diffusion which are some extensions of the classical competition prey predator and cooperating ecological systems the monotone iterative schemes lead to some true positive solutions of the competition system and to quasisolutions of the prey predator and cooperating systems also given are some sufficient conditions for the existence of a unique positive solution to each of the three model problems

pseudo markov systems and infinitely generated schottky groups in this paper we extend the theory of conformal graph directed markov systems to what we call conformal pseudo markov systems these systems may have a countable infinite set of edges and unlike graph directed markov systems they may also have a countable infinite set of vertices our first goal is to develop suitable symbolic dynamics which we then use to analyze conformal pseudo markov systems by giving extensions of various aspects of the thermodynamic formalism and of fractal geometry most important by establishing the existence of a unique conformal measure along with its invariant version we obtain a generalization of bowen s formula concerning the hausdorff dimension of the limit set of a conformal pseudo markov system here we also obtain an interesting formula for the closure of the limit set finally we give some applications of our analysis to the theory of kleinian groups we show that there exists a rather exotic class of infinitely generated schottky groups of the second kind acting on d 1 dimensional hyperbolic space containing groups with limit sets of hausdorff dimension equal to any given number t leq d whereas their poincar e exponent can be less than any given positive number s t moreover we show that the dissipative part of the limit sets of these groups has further interesting properties

the first eigenvalue in a tower of coverings soit m une variete de riemann compacte et soit m i une famille d espaces de recouvrement riemanniens finis de m soit 1 m i la premiere valeur propre du laplacien sur m i on cherche l existence d une suite de i ou 1 m i est borne inferieurement

analysis of a population model with strong cross diffusion in unbounded domains we study a parabolic population model in the full space and prove the global in time existence of a weak solution this model consists of two strongly coupled diffusion equations describing the population densities of two competing species the system features intrinsic growth inter and intra specific competition of the species as well as diffusion cross diffusion and self diffusion and drift terms related to varying environment quality the cross diffusion terms can be large making the system non parabolic for large initial data for the first time solutions in unbounded domains are studied the method of our proof is a combination of a time semi discretization a transformation of the system guaranteeing the positivity of the solution a special entropy symmetrizing the system and compactness arguments 2000 mathematics subject classification 35k55 primary 92d25 35d05 secondary

semi discretization in time and numerical convergence of solutions of a nonlinear cross diffusion population model a positivity preserving numerical scheme for a strongly coupled cross diffusion model for two competing species is presented based on a semi discretization in time the variables are the population densities of the species existence of strictly positive weak solutions to the semidiscrete problem is proved moreover it is shown that the semidiscrete solutions converge to a non negative solution of the continuous system in one space dimension the proofs are based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

time delayed parabolic system in a two species competitive model with stage structure a two species competitive model with stage structure is discussed the dynamics of coupled system of semilinear parabolic equations with time delays are investigated results on the local and global stabilities of the axial equilibria and positive equilibrium are given our results show that the introduction of diffusion does not affect the permanence and extinction of the species though the introduction of stage structure brings negative effect on it

an initial boundary value problem for a certain density dependent diffusion system on considere le systeme parabolique quasilineaire u t x c 1 d 1 v v e 1 a 1 v b 1 u u v t x c 2 d 2 u v e 2 a 2 u b 2 o v dans o t u x s 0 v x s sur o t u x o w 1 x v x o w 2 x sur ou r n est un domaine borne a frontiere lisse