unimodal dynamical systems comparison principles spreading speeds and travelling waves abstract reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity for such non monotone dynamical systems we develop a general comparison principle and show how this general comparison principle coupled with some existing results for monotone dynamical systems can be used to establish results on the asymptotic speeds of spread and travelling waves we illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain with the non monotone nonlinearities including the ricker birth function and the mackey glass hematopoiesis feedback

abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

note on coherent states and adiabatic connections curvatures we give a possible generalization to the example in the paper of zanardi and rasetti phys lett a 264 94 1999 for this explicit forms of adiabatic connection curvature etc are given we also discuss the possibility of another generalization of their model

a geometric approach in the study of traveling waves for some classes of non monotone reaction diffusion systems abstract in this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non monotone reaction diffusion systems our approach consists of two steps first we develop a geometrical shooting argument with the aid of the theorem of homotopy invariance on the fundamental group to obtain the positive semi traveling wave solutions for a large class of reaction diffusion systems including the models of predator prey interaction for both predator independent dependent functional responses the models of combustion belousov zhabotinskii reaction si type of disease transmission and the model of biological flow reactor in chemostat next we apply the results obtained from the first step to some models such as the beddinton deangelis model and the model of biolocal flow reactor to show the convergence of these semi traveling wave solutions to an interior equilibrium point by the construction of a lyapunov type function or the convergence of semi traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi traveling wave solutions

existence and uniqueness of travelling waves for a neural network a one dimensional scalar neural network with two stable steady states is analysed it is shown that there exists a unique monotone travelling wave front which joins the two stable states some additional properties of the wave such as the direction of its velocity are discussed

chern simons solitons toda theories and the chiral model the two dimensional self dual chern simons equations are equivalent to the conditions for static zero energy solutions of the 2 1 dimensional gauged nonlinear schrodinger equation with chern simons matter gauge dynamics in this paper we classify all finite chargesu n solutions by first transforming the self dual chern simons equations into the two dimensional chiral model or harmonic map equations and then using the uhlenbeck wood classification of harmonic maps into the unitary groups this construction also leads to a new relationship between thesu n toda andsu n chiral model solutions

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

subsonic solutions to a one dimensional non isentropic hydrodynamic model for semiconductors the one dimensional stationary full hydrodynamic model for semiconductor devices with non isentropic pressure is studied this model consists of the equations for the electron density electron temperature and electric field in a bounded domain supplemented with boundary conditions the existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations non constant and constant heat conductivities moreover we prove uniqueness of a classical solution in the latter case the existence proofs are based on elliptic estimates stampacchia truncation methods and fixed point arguments

regular traveling waves for a nonlocal diffusion equation abstract in this paper we study a nonlocal diffusion equation with a general diffusion kernel and delayed nonlinearity and obtain the existence nonexistence and uniqueness of the regular traveling wave solutions for this nonlocal diffusion equation as an application of the results we reconsider some models arising from population dynamics epidemiology and neural network it is shown that there exist regular traveling wave solutions for these models respectively this generalized and improved some results in literatures

traveling waves for a nonlocal dispersal sir model with delay and external supplies this paper is concerned with the existence nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed sir model with constant external supplies and holling ii incidence rate we find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c but also by the so called basic reproduction number r 0 of the corresponding reaction system that is we establish the existence of traveling waves for r 0 1 and each wave speed c c and the nonexistence for r 0 1 and any 0 c c or r 0 1 we also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed biologically speaking the longer the latency of infection in a vector is the slower the disease spreads

a nonlocal diffusion model of a single species with age structure abstract using theory of fourier transformation dirac function and von foerster rule with nonlocal diffusion operator we derive a single species population model with two age stages juvenile and mature which includes nonlocal dispersal both in diffusion and reaction we found that the nonlocal reaction kernel function for mature population depends on the kernel function of diffusion for two age stages this model takes the local diffusion model with only laplacian operator or laplacian operator combining with convection operator as particular examples the existence uniqueness positivity and boundedness of initial value problem are also investigated in the present article as a new model its dynamics is worthy to be explored in the future work

on the existence of traveling waves for delayed reaction diffusion equations abstract we study the existence of traveling wave solutions for reaction diffusion equations with nonlocal delay where reaction terms are not necessarily monotone the existence of traveling wave solutions for reaction diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the schauder fixed point theorem the smoothness of upper and lower solutions is not required in this paper

stability of periodic steady state solutions to a non isentropic euler poisson system abstract we study the stability of periodic smooth solutions near non constant steady states for a non isentropic euler poisson system without temperature damping term the system arises in the theory of semiconductors for which the doping profile is a given smooth function in this stability problem there are no special restrictions on the size of the doping profile but only on the size of the perturbation we prove that small perturbations of periodic steady states are exponentially stable for large time for this purpose we introduce new variables and choose a non diagonal symmetrizer of the full euler equations to recover dissipation estimates this also allows to make the proof of the stability result very simple and concise

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species abstract we discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species we consider not only the mass and momentum equations for electrons but also those two equations for holes the recombination effects between electrons and holes are taken into consideration as well we study the case where the doping profile is close to zero and depends on the spacial variable x we shall show that steady state solutions are asymptotically stable

symplectic manifolds coherent states and semiclassical approximation the symplectic structure and hamiltonian dynamics for a class of grassmannian manifolds are described here using the two dimensional sphere s2 and disc d2 as illustrative cases we write their path integral representations using coherent state techniques these path integrals can be evaluated exactly by semiclassical methods thus providing examples of the localization formula along the way we also give a local coordinate description for a class of grassmannians

asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors abstract we study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included we study the case where the flow is subsonic and the doping profile is close to a negative constant depending on the spacial variablex we shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfiesp 0 wherepis defined in 3 5

coherent states path integral and semiclassical approximation using the generalized coherent states it is shown that the path integral formulas for su 2 and su 1 1 in the discrete series are wkb exact if it is started from the trace of e it where h is given by a linear combination of generators in this case the wkb approximation is achieved by taking a large spin limit j k under which it is found that each coefficient vanishes except the leading term which indeed gives the exact result it is further pointed out that the discretized form of path integral is indispensable in other words the continuum path integral expression sometimes leads to a wrong result therefore great care must be taken when some geometrical action would be adopted even if it is so beautiful as the starting ingredient of path integral discussions on generalized coherent states are also presented both from geometrical and simple oscillator schwinger boson points of view

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

existence and uniqueness of traveling waves for non monotone integral equations with applications abstract a class of integral equations without monotonicity is investigated it is shown that there is a spreading speed c 0 for such an integral equation and that its limiting integral equation admits a unique traveling wave up to translation with speed c c and no traveling wave with c c these results are also applied to some nonlocal reaction diffusion population models

solutions of a toda equations based on noncompact group su 1 1 and infinite dimensional grassmann manifolds special solutions of a toda equations are constructed based on noncompact group su 1 1 these solutions are derived from the holomorphic construction of infinite dimensional nonlinear grassmann models it is also shown that the solutions give a family of solutions of self dual einstein equations in a certain continuum limit

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

separation dichotomy and wavefronts for a nonlinear convolution equation abstract this paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models first we prove that at each end of the real line every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero this dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi wavefront solutions to the convolution equation finally we apply our theoretical results to several well studied classes of evolution equations with asymmetric non local and non monotone response we show that contrary to the symmetric case these equations can possess simultaneously stationary expansion and extinction waves

spreading speed for a nonlocal diffusive delayed model without quasi monotonicity abstract in this article we study the spatial spreading dynamics for a nonlocal diffusive equation with general nonmonotone monostable nonlinearity on the basis of a sandwich technique and a comparison theorem for solutions of the cauchy problems of three systems the spreading speed c is established for the model as an application of the results we consider some models as special cases it is shown that the results in this article generalize and improve some results in the existing literature

stability of travelling wave solutions of diffusive predator prey systems the stability of travelling wave solutions of singularly perturbed diffusive predator prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue at a 0 is simple the proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues

the asymptotic behavior of global smooth solutions to the hydrodynamic model for semiconductors with spherical symmetry abstract in this paper we study the asymptotic behavior of the global smooth solutions to the initial boundary value problem for the hydrodynamic model for semiconductors with spherical symmetry we prove that the solution to the problem converges to a stationary solution time asymptotically exponentially fast

traveling waves in a nonlocal dispersal population model with age structure abstract this paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age structure if the birth function is monotone then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness it is proved that the traveling wavefront is strictly increasing and unique up to a translation the asymptotic behavior of traveling wavefronts is also obtained if the birth function is not monotone the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi monotonicity

entire solutions for nonlocal dispersal equations with spatio temporal delay monostable case abstract this paper deals with entire solutions for a general nonlocal dispersal monostable equation with spatio temporal delay i e solutions that are defined in the whole space and for all time t r we first derive a particular model for a single species and show how such systems arise from population biology then we construct some new types of entire solutions other than traveling wave solutions and equilibrium solutions of the equation under consideration with quasi monotone and non quasi monotone nonlinearities various qualitative properties of the entire solutions are also investigated in particular the relationship between the entire solutions and the traveling wave fronts which they originated is considered our main arguments are based on the comparison principle the method of super and sub solutions and the construction of auxiliary control systems

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

convergence of the nonisentropic euler poisson equations to incompressible type euler equations abstract in this paper we investigate a multidimensional nonisentropic hydrodynamic euler poisson model for semiconductors we study the convergence of the nonisentropic euler poisson equation to the incompressible nonisentropic euler type equation via the quasi neutral limit the local existence of smooth solutions to the limit equations is proved by an iterative scheme the method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit

monostable waves in a class of non local convolution differential equation abstract the current paper is devoted to the study of wave propagation dynamics for a class of convolution equation with monostable structure it is shown that this equation admits traveling wave solution connecting the zero steady state even when the nonlinear term of this equation is without monotonicity a sufficient condition for the traveling wave solution that converges to the positive steady state is also established

traveling waves for non local delayed diffusion equations via auxiliary equations in this paper we study the existence of traveling wave solutions for a class of delayed non local reaction diffusion equations without quasi monotonicity the approach is based on the construction of two associated auxiliary reaction diffusion equations with quasi monotonicity and a profile set in a suitable banach space by using the traveling wavefronts of the auxiliary equations under monostable assumption by using the schauder s fixed point theorem we then show that there exists a constant c 0 such that for each c c the equation under consideration admits a traveling wavefront solution with speed c which is not necessary to be monotonic

nonmonotone travelling waves in a single species reaction diffusion equation with delay abstract we prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction diffusion equations u t t x u t x u t x g u t h x when g c 2 r r has exactly two fixed points x 1 0 and x 2 k 0 recently nonmonotonic waves were observed in numerical simulations by various authors here for a wide range of parameters we explain why such waves appear naturally as the delay h increases for the case of g with negative schwarzian our conditions are rather optimal we observe that the well known mackey glass type equations with diffusion fall within this subclass of as an example we consider the diffusive nicholson s blowflies equation

existence of traveling wave solutions for diffusive predator prey type systems abstract in this work we investigate the existence of traveling wave solutions for a class of diffusive predator prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions the profile equations for the above system can be reduced as a four dimensional ode system and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theory we obtain the existence results our results can apply to various kinds of ecological models