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

bifurcation analysis on a two neuron system with distributed delays abstract a general two neuron model with distributed delays is studied in this paper its local linear stability is analyzed by using the routh hurwitz criterion if the mean delay is used as a bifurcation parameter we prove that hopf bifurcation occurs for a weak kernel this means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value the direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical analysis are also given

existence of solutions for impulsive neutral functional differential equations with nonlocal conditions abstract the existence uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal cauchy problem in general banach spaces are studied by using the fixed point technique and semigroup of operators

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

on the stabilization of an overhead crane system with dynamic and delayed boundary conditions this article is dedicated to the investigation of long time behavior of an overhead crane with input delays in the boundary control contrary to previous works the compensating terms in the proposed feedback control law are not of the same type as the delayed term next the closed loop system is shown to be well posed in the sense of semigroups theory furthermore the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data is obtained by applying lasalle s invariance principle then the convergence rate is shown to be exponential by means of the frequency domain method the asymptotic distribution of the eigenvalues as well as the eigenfunctions of the system are also provided based on which the differentiability of its semigroup is proved and hence the spectrum determined growth condition holds finally the outcomes are illustrated by a set of numerical simulations

order parameter distribution function of finite o n symmetric systems in an external field abstract we study the effect of an external field h on the order parameter distribution function near the critical point of o n symmetric three dimensional 3d systems in a finite geometry the distribution function is calculated within the 4 field theory for a 3d cube with periodic boundary conditions by means of a new approach that appropriately deals with the goldstone modes below tc the result describes finite size effects near the critical point in the h t plane including the first order transition at the coexistence line at h 0 below tc theoretical predictions of the finite size scaling function are presented for the ising n 1 and xy n 2 models good agreement is found with recent monte carlo data for the distribution function of the magnetization of the 3d ising model at finite h above and below tc

the 1 1 resonance in hamiltonian systems abstract two degree of freedom hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation considering the frequencies as parameters the system undergoes a bifurcation when the frequencies pass through a resonance these bifurcations are well understood for most resonances k l but not the semisimple cases 1 1 and 1 1 a two degree of freedom hamiltonian system can be approximated to any order by an integrable normal form the reason is that the normal form of a hamiltonian system has an additional integral due to the normal form symmetry the latter is intimately related to the ratio of the frequencies for a rational frequency ratio this leads to s 1 symmetric systems the question we wish to address is about the co dimension of such a system in 1 1 resonance with respect to left right equivalence where the right action is s 1 equivariant the result is a co dimension five unfolding of the central singularity two of the unfolding parameters are moduli and the remaining non modal parameters are the ones found in the linear unfolding of this system

global solutions for abstract neutral differential equations we study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis some concrete applications related to ordinary and partial differential equations are considered

existence and stability for some partial neutral functional differential equations with infinite delay abstract in this paper we study a class of partial neutral functional differential equations with infinite delay we suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the hille yosida theorem we give some sufficient conditions ensuring the existence uniqueness and regularity of solutions a principle of linearized stability is also established in the autonomous case to illustrate our abstract results we conclude this work by an example

global asymptotic behavior of a chemostat model with discrete delays this paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat the model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations in the case where only two species are engaged in competition it is shown that competitive exclusion holds for any monotone growth response functions sufficient conditions are also obtained for the model to exhibit competitive exclusion in the n species case in regard to the delay effects on the qualitative outcome of competition it is demonstrated that when the delays are relatively small the predictions of the model are identical with the predictions given by corresponding models without time delays however including large delays in the model may alter the predicted outcome of competition the techniques used also work when different removal rates are permitted an

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equation in banach spaces in this paper we prove some existence results for almost automorphic and pseudo almost automorphic mild solutions to a class of abstract differential equations in banach spaces the main technique is based on some composition theorems combined with the contraction mapping theorem finally we present an application to a semilinear partial differential equation with dirichlet conditions

periodic trajectories of distributed parameter biochemical systems with time delay abstract this paper deals with a model of a biochemical reactor system with distributed parameters and with a time delay in the growth response time delay has been introduced in microbial growth systems to explain the time lapse between the consumption of liquid substrate and its conversion to solid biomass we study here the properties of the resulting system of partial functional differential equations we first prove the existence positivity and a compactness property of the system trajectories we then prove the existence of periodic solutions of the system for large values of the delay numerical simulations illustrate the existence of such solutions

lie poisson structures dual spin spacecraft and asymptotic stability on traite la dynamique d un astronef rigide portant trois rotors a partir des equations dynamiques on deduit les structures de lie poisson

global dynamics of a mathematical model of competition in the chemostat general response functions and differential death rates a model of exploitative competition of n species in a chemostat for a single essential nonreproducing growth limiting resource is considered s b hsu siam j appl math 34 1978 pp 760 763 applies lasalle s extension theorem of lyapunov stability theory to study the asymptotic behavior of solutions in the special case that the response functions are modeled by michaelis menten dynamics g j butler and g s k wolkowicz siam j appl math 45 1985 pp 138 151 on the other hand allow more general response functions including monotone and nonmonotone functions but their analysis requires the assumption that the death rates of all the species are negligible in comparison with the washout rate and hence can be ignored by means of lyapunov stability theory the global dynamics of the model for a large class of response functions are studied including both monotone and nonmonotone functions though it is not as general as the class studied by butler and wolkowicz and the results in

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

existence of solutions of nonlinear abstract neutral integrodifferential equations in this paper we establish a set of sufficient conditions for the existence of mildsolutions of nonlinear neutral integrodifferential equations in banach spaces by using the schaefer fixed point theorem an application is provided to illustrate the theory

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

failure of universal finite size scaling above the upper critical dimension abstract previous theories have predicted that o n symmetric systems in a finite cubic geometry with periodic boundary conditions have universal finite size scaling functions near criticality in d 4 dimensions on the basis of exact results for the o n symmetric 4 model in the large n limit we show that universal finite size scaling does not hold in the predicted form because of significant cut off and lattice effects for d 4 it is shown that finite size scaling is valid with two reference lengths which turn out to be identical with the amplitudes of the bulk correlation length for the 4 field theory the finite size scaling functions are shown to be non universal i e to depend explicitly on the cut off and on the bare four point coupling constant whereas for a 4 lattice model the finite size scaling functions have a different form that is independent of the lattice spacing and the four point coupling constant

stability and bifurcation analysis of a reaction diffusion equation with spatio temporal delay abstract the spatio temporal patterns of a general reaction diffusion equation with non local delay are considered by analyzing the characteristic equations and applying the complex plane theory the stability of the constant steady state and the possible hopf bifurcations are obtained with the mean delay as a bifurcation parameter the absolute stable conditional stable and unstable region can be explicitly divided by the coefficients of the term without delay and the term with non local delay by investigating the effect of any weight function on the dynamics of the system we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions and the algorithm for determining the direction and stability of hopf bifurcation is derived by computing the normal form on the center manifold the result shows that for the case of strong kernel the average delay may induce the stability switches finally the theoretical results are applied to a diffusive food limited population model numerical simulations show the existence of the orbit connecting the unstable spatially inhomogeneous periodic solutions to stable spatially homogeneous periodic solutions

field theory of finite size effects for systems with a one component order parameter the field theoretic renormalization group approach is used to describe finite size effects near the critical point of the 4 model with a one component order parameter problems of previous perturbation approaches for t tc are discussed and an improved perturbation theory is employed that is applicable both above and below tc the susceptibility order parameter specific heat and a cumulant ratio are calculated for fixed d 4 in one loop order for the case of a cube with periodic boundary conditions finite size scaling functions are evaluated in three dimensions without using the e 4 d expansion quantitative agreement with monte carlo mc data of the three dimensional ising model is found in most cases additional mc data of larger systems would be desirable in order to test the detailed predictions of the finite size field theory more conclusively in the asymptotic region

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

simulation of static critical phenomena in nonideal fluids with the lattice boltzmann method a fluctuating nonideal fluid at its critical point is simulated with the lattice boltzmann method it is demonstrated that the method employing a ginzburg landau free energy functional correctly reproduces the static critical behavior associated with the ising universality class a finite size scaling analysis is applied to determine the critical exponents related to the order parameter compressibility and specific heat a particular focus is put on finite size effects and issues related to the global conservation of the order parameter

the linear and nonlinear diffusion of the competitive lotka volterra model abstract this paper has studied the effects of linear and nonlinear diffusion of the competitive lotka volterra model and has investigated how the linear and nonlinear diffusions lead from the extinction of one species to the persistence or global asymptotic stability of all species this research has important implications in the design of nature reserves

hopf bifurcation analysis of a turbidostat model with discrete delay in this contribution the dynamic behaviors of a turbidostat model with discrete delay are investigated with the delay of digestion chosen to be a bifurcation parameter we find that hopf bifurcations occur when the delay crosses some critical values also by employing the normal form theory and the center manifold theorem we determine the type and stability of the bifurcating periodic solutions finally numerical simulations are offered to support our results

a mechanical system with a wild horseshoe we consider a gyrostat in its simplest form namely a rigid body with a flywheel attached it is well known that although the motions are coupled when the rotor is symmetric the full system is completely integrable in terms of elliptic functions the euler equations for the angular momentum components with respect to the rigid body now depend on the parameter i angular momentum of the flywheel a constant of motion and the phase portrait of the system undergoes several bifurcations analytical formulas in terms of elementary functions can be given for the separatrices a small imperfection in the flywheel breaks the s1 symmetry as a result the separatrices split with transversal intersection producing horseshoes we applied the techniques of holmes and marsden to write down the melnikov function of the system the integral is computed by the method of residues in the limit case i 0 somewhat surprisingly the amplitude of the melnikov function diverges we propose an explanation for this par

existence of solutions for impulsive partial neutral functional differential equation with infinite delay abstract in this paper the existence of mild solutions for first order impulsive semilinear neutral functional differential equations with infinite delay in banach spaces is investigated we derive conditions in respect of the hausdorff measure of noncompactness under which the mild solutions exist in banach spaces our results improve and generalize some previous results

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

boundary effects in the three dimensional ising model abstract simulations of the standard three dimensional ising model with a variety of boundary conditions for medium and large systems are compared with field theoretical predictions in particular setting boundary spins equal to zero is not the best approximation for the dirichtet boundary condition of zero magnetization at the boundary the simulations for the specific heat agree semiquantitatively with the field theory for periodic and dirichtet boundary conditions

competition in the chemostat global asymptotic behavior of a model with delayed response in growth the asymptotic behavior of solutions of a model for competition between two microorganisms in the chemostat is studied the model incorporates time delays that allow for the cellular components of each competing species to be structured to include unassimilated or stored nutrient sufficient conditions on the parameters of the model that guarantee i competitive exclusion and ii persistence of at least one of the competing organisms are determined the results extend earlier results on the corresponding model for a single species and also extend these to include competition

finite size scaling of the interfacial tension the interfacial free energy appropriate to a finite system in the ising universality class is calculated to one loop order consideration is given to the behavior in both three and four dimensions via an epsilon expansion the results corresponding to three dimensions are compared with the simulation data of mon and jasnow

competition in the chemostat a distributed delay model and its global asymptotic behavior in this paper we propose a two species competition model in a chemostat that uses a distributed delay to model the lag in the process of nutrient conversion and study the global asymptotic behavio

existence of solutions of nonlinear neutral integrodifferential equations in banach spaces abstract in this paper we prove the existence of mild solutions of a nonlinear neutral integrodifferential equation in a banach space the results are obtained by using the schaefer fixed point theorem as an application the controllability problem for the neutral system is discussed

existence of periodic solutions for abstract neutral non autonomous equations with infinite delay in this paper by using sadovskii fixed point theorem we study the existence of solutions and periodic solutions for a class of abstract neutral functional evolution equations with infinite delay an example is presented in the end to show the applications of the obtained results

asymptotic behavior and stability for solutions of a biochemical reactor distributed parameter model this paper deals with the dynamical analysis of a tubular biochemical reactor the existence of nonnegative state trajectories and the invariance of the set of all physically feasible state values under the dynamical equation as well as the convergence of the state trajectories to equilibrium profiles are proved in addition the existence of multiple equilibrium profiles is analyzed it is proved that under physically meaningful conditions the system has two stable and one unstable equilibrium profiles

phase flow of an axially symmetrical gyrostat with one constant rotor we analyze the attitude dynamics of an axially symmetric gyrostat under no external forces and one constant internal spin we introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere with these coordinates we realize that the problem belongs to a general class of hamiltonian systems namely the problem here considered is the one parameter hamiltonian that is a polynomial of at most degree two in a base of the lie algebra so 3 the parametric bifurcations are found for both cases when the rotor is spinning about the axis of symmetry of the gyrostat and when it is spinning about another axis of inertia the general solution for the global general flow is expressed in terms of the jacobian elliptic functions

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

coexistence in a model of competition in the chemostat incorporating discrete delays a model of two species competing for a single nutrient in the chemostat is proposed incorporating general monotone uptake functions with discrete time delays after transforming the model an anal

global periodic solutions for a differential delay system modeling a microbial population in the chemostat abstract we show that nonconstant periodic solutions of the delay differential system modeling a microbial population in the chemostat s t 1 s t p s t u t u t u t 1 p s t exist whenever the positive equilibrium is unstable

existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations abstract some sufficient conditions for the existence and uniqueness of pseudo almost periodic mild solutions to some classes of partial evolution equations are given we then make use of our abstract results to discuss the existence of pseudo almost periodic solutions to some partial differential equations

critical phenomena with convergent series expansions in a finite volume linked cluster expansions are generalized from an infinite to a finite volume they are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase a new criterion is proposed to distinguish first from second order transitions within a finite size scaling analysis the criterion applies also to other methods for investigating the phase structure such as monte carlo simulations our computational tools are illustrated with the example of scalar o n models with four and six point couplings forn 1 andn 4 in three dimensions it is shown how to localize the tricritical line in these models we indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity

on the stability of a periodic solution of distributed parameters biochemical system this paper studies the stability of periodic solutions of distributed parameters biochemical system with periodic input sin t we prove that if sin t is periodic then the system has a periodic solution that is input to state stable when small perturbations are acting on the input concentration sin t

stability of the permanent rotations of an asymmetric gyrostat in a uniform newtonian field the stability of the permanent rotations of a heavy gyrostat is analyzed by means of the energy casimir method sufficient and necessary conditions are established for some of the permanent rotations the geometry of the gyrostat and the value of the gyrostatic moment are relevant in order to get stable permanent rotations moreover the necessary conditions are also sufficient for some configurations of the gyrostat

the reversible umbilic bifurcation abstract hamiltonian systems with several degrees of freedom regularly lead to the investigation of bifurcating equilibria in reduced one degree of freedom systems this paper concerns equilibria with vanishing linearisation a co dimension two phenomenon in the reversible context under appropriate transversality conditions such equilibria have versal unfoldings related to the elliptic and hyperbolic umbilic catastrophes this has applications to gyrostat motion and also helps to explain the dynamics defined by the normal form of the henon heiles system the occurring unfoldings turn out to be versal even in the general reversible context of not necessarily hamiltonian systems

bifurcation analysis of a chemostat model with a distributed delay a chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed the model incorporates a general nutrient uptake function and a distributed delay the delay indicates that the growth of the species depends on the past concentration of nutrient using the average time delay as a bifurcation parameter it is proven that the model undergoes a sequence of hopf bifurcations stability criteria for the bifurcating periodic solutions are derived it is also found that the periodic solutions become unstable if the dilution rate is increased computer simulations illustrate the results

diversity of critical behavior within a universality class we study spatial anisotropy effects on the bulk and finite size critical behavior of the mathrm o n symmetric anisotropic ensuremath varphi 4 lattice model with periodic boundary conditions in a d dimensional hypercubic geometry above at and below t c the absence of two scale factor universality is discussed for the bulk order parameter correlation function the bulk scattering intensity and for several universal bulk amplitude relations the anisotropy parameters are observable by scattering experiments at t c for the confined system renormalization group theory within the minimal subtraction scheme at fixed dimension d for 2ldl4 is employed in contrast to the ensuremath epsilon 4 ensuremath d expansion the fixed d finite size approach keeps the exponential form of the order parameter distribution function unexpanded for the case of cubic symmetry and for n 1 our perturbation approach yields excellent agreement with the monte carlo mc data for the finite size amplitude of the free energy of the three dimensional ising model at t c by mon phys rev lett 54 2671 1985 the ensuremath epsilon expansion result is in less good agreement below t c a minimum of the scaling function of the excess free energy is found we predict a measurable dependence of this minimum on the anisotropy parameters the relative anisotropy effect on the free energy is predicted to be significantly larger than that on the binder cumulant our theory agrees quantitatively with the nonmonotonic dependence of the binder cumulant on the ferromagnetic next nearest neighbor nnn coupling of the two dimensional ising model found by mc simulations of selke and shchur j phys a 38 l739 2005 our theory also predicts a nonmonotonic dependence for small values of the antiferromagnetic nnn coupling and the existence of a lifshitz point at a larger value of this coupling the nonuniversal anisotropy effects in the finite size scaling regime are predicted to satisfy a kind of restricted universality the tails of the large l behavior at t ensuremath ne t c violate both finite size scaling and universality even for isotropic systems as they depend on the bare four point coupling of the ensuremath varphi 4 theory on the cutoff procedure and on subleading long range interactions

comparison between finite size field theory and monte carlo simulations for the three dimensional ising model abstract recent field theoretic predictions of finite size effects for various thermodynamic quantities near the critical point are compared with new accurate monte carlo mc data for the l l l ising model obtained from a cluster algorithm special purpose computer owing to the large size l 32 64 128 256 of the ising models these mc data permit to test the finite size field theory in the asymptotic scaling region above and below t c the results constitute the most accurate confirmation of finite size scaling in three dimensions obtained to date in a wide range of temperatures agreement with the predicted shape of the finite size scaling functions is found on a quantitative level

stable oscillations in a predator prey model with time lag the lotka volterra model with carrying capacity at the prey and time delay in the equation concerning the predator is considered the time delay is taken into consideration by an integral with the weight function a exp at it is shown that under certain conditions imposed upon the parameters of the system a supercritical hopf bifurcation takes place at a certain value a0 of a and the bifurcating closed paths are orbitally asymptotically stable for values of a below a0

geometric transformations and new integrable problems of rigid body dynamics the problem of motion of a rigid body about a fixed point under the action of conservative forces is considered in the case admitting a linear integral but no axis of symmetry neither in space nor in the body is present a simple transformation of the configuration space is used to reduce the problem of motion of the body to another problem concerning the same body under a system of axisymmetric forces this analogy enables the construction of several new integrable cases of the first problem by transforming certain known ones of the second the new cases usually involve singular potential terms integrals of motion and physical interpretation are given explicitly for one generally integrable case other general and conditional cases are pointed out

approximations of solutions to neutral functional differential equations with nonlocal history conditions abstract this work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a hilbert space the approximation of solution to a class of such problems is studied moreover the convergence of faedo galerkin approximation of solution is shown for illustration an example is worked out

existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations abstract in this paper under acquistapace terreni conditions we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients