zeros of accretive operators and asymptotics of a second order difference inclusion in banach spaces abstract by developing new methods we investigate the asymptotic behavior of solutions to a general second order difference inclusion of accretive type and apply the results to approximate zeros of accretive operators in banach spaces and to optimization problems our results extend some previously known results in hilbert and banach spaces

central limit theorems for infinite series of queues and applications to simple exclusion we prove that a tagged particle in asymmetric simple exclusion satisfies a central limit theorem when properly rescaled to obtain this result we derive several results of positive or negative correlation for occupation times of a server in a series of queues which imply various central limit theorems

the simple exclusion process as seen from a tagged particle on considere le processus d exclusion simple comme ou a partir d une particule marquee on determine l ensemble des mesures invariantes et invariantes par translation sur z d

stationary half space last passage percolation in this paper we study stationary last passage percolation with exponential weights and in half space geometry we determine the limiting distribution of the last passage time in a critical window close to the origin the result is a new two parameter family of distributions one parameter for the strength of the diagonal bounding the half space strength of the source at the origin in the equivalent tasep language and the other for the distance of the point of observation from the origin it should be compared with the one parameter family giving the baik rains distributions for full space geometry we finally show that far enough away from the characteristic line our distributions indeed converge to the baik rains family we derive our results using a related inhomogeneous integrable model having pfaffian correlations together with careful analytic continuation and steepest descent analysis

shift equivalence of measures and the intrinsic structure of shocks in the asymmetric simple exclusion process we investigate the properties of non translation invariant measures describing particle systems on mathbb z which are asymptotic to different translation invariant measures on the left and on the right often the structure of the transition region can only be observed from a point of view which is random in particular configuration dependent two such measures will be called shift equivalent if they differ only by the choice of such a viewpoint we introduce certain quantities called translation sums which under some auxiliary conditions characterize the equivalence classes our prime example is the asymmetric simple exclusion process for which the measures in question describe the microscopic structure of shocks in this case we compute explicitly the translation sums and find that shocks generated in different ways in particular via initial conditions in an infinite system or by boundary conditions in a finite system are described by shift equivalent measures we show also that when the shock in the infinite system is observed from the location of a second class particle treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures

random walk of second class particles in product shock measures we consider shock measures in a class of conserving stochastic particle systems on these shock measures have a product structure with a step like density profile and include a second class particle at the shock position we show for the asymmetric simple exclusion process for the exponential bricklayers process and for a generalized zero range process that under certain conditions these shocks and therefore the second class particles perform a simple random walk some previous results including random walks of product shock measures and stationary shock measures seen from a second class particle are direct consequences of our more general theorem multiple shocks can also be handled easily in this framework similar shock structure is also found in a nonconserving model the branching coalescing random walk where the role of the second class particle is played by the rightmost or leftmost particle

convergence and local equilibrium for the one dimensional nonzero mean exclusion process we consider finite range nonzero mean one dimensional exclusion processes on we show that if the initial configuration has density then the process converges in distribution to the product bernoulli measure with mean density from this we deduce the strong form of local equilibrium in the hydrodynamic limit for non product initial measures

second order differential equations on r governed by monotone operators abstract consider in a real hilbert space h the differential equation e p t u t q t u t a u t f t for a a t r 0 with the condition u 0 x d a where a d a h h is a possibly set valued maximal monotone operator with 0 0 a or more generally 0 r a p q l r with ess inf p 0 and either ess inf q 0 or ess sup q 0 recall that equation e in the case p 1 q 0 f 0 subject to u 0 x and sup t 0 u t was investigated in the early 1970s by v barbu who derived in particular from his results a definition for the square root of the nonlinear operator a subsequently h brezis n h pavel l veron and others have paid attention to equation e in this paper we prove the existence and uniqueness of the solution to equation e subject to u 0 x d a in the weighted space x l b 2 r h where b t a t p t a t exp 0 t q s p s d s under our weak assumptions on p and q see above and f x for x d a we prove the existence of a generalized solution this is a classic solution if p 1 q c r 0 if p 1 q t c r 0 f 0 the solutions give rise to a nonlinear semigroup of contractions if a is linear its infinitesimal generator g is given by g c 2 i c 2 4 i a

shock fluctuations in asymmetric simple exclusion the one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the burgers equation we study the process with rates of jumpsp q to the right and left respectively and with initial product measure with densities to the left and right of the origin respectively with shock initial conditions we prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times if this particle is added at another site then it describes the behavior of a characteristic of the burgers equation for vanishing left density 0 we prove in the scale t1 2 that the position of the shock at timet depends only on the initial configuration in a region depending ont the proofs are based on laws of large numbers for the second class particle

annihilation diffusion processes an exactly solvable model a family of diffusion annihilation processes is introduced which is exactly solvable this family contains parameters that control the diffusion and annihilation rates the solution is based on the bethe ansatz and using special boundary conditions to represent the reaction the processes are investigated both on the lattice and on the continuum special cases of this family of processes are the simple exclusion process and the drop push model

convergence of solutions to a second order difference inclusion abstract we investigate the asymptotic behavior of solutions to the following second order difference inclusion u i 1 1 i u i i u i 1 c i a u i i 1 u 0 x sup i 0 u i where a is a maximal monotone operator in a real hilbert space h and c i and i are positive real sequences we show weak and strong convergence of solutions to an element of a 1 0 for general maximal monotone operator and when a where is a convex proper and lower semicontinuous function our results extend and improve previous results by morosanu 1979 18 mitidieri morosanu 1985 86 23 see also morosanu 1988 1 pp 156 168 and aperutesei 2003 21 22 as well as some recent works of djafari rouhani khatibzadeh 2010 2011 25 26 and khatibzadeh 2011 27 with more general assumptions on parameters c i and i in homogeneous case

unstructured grid generation using iterative point insertion and local reconnection a procedure is presented for efficient generation of high quality two or three dimensional unstructured grids of triangular or tetrahedral elements the present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing front type point placement initially the connectivity for these generated points is obtained by directly subdividing the elements which contain them without regard to quality this connectivity is then improved by iteratively using local reconnection subject to a quality criterion for two dimensions a min max criterion is used and for three dimensions a delaunay in sphere criterion followed by a min max type criterion is used the overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution grid quality and performance statistics are presented for a variety of two and three dimensional configurations the combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods

shock fluctuations in the asymmetric simple exclusion process we consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively q p ferrari et al 1991 have shown that if the initial measure isv a product measure with densities and to the left and right of the origin respectively then there exists a microscopic shock for the system a shock is a random positionx t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively uniformly int we compute the diffusion coefficient of the shockd lim t t 1 e x t 2 ex t 2 and findd p q 1 1 1 as conjectured by spohn 1991 we show that in the scale sqrt t the position ofx t is determined by the initial distribution of particles in a region of length proportional tot we prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and this is the so called dynamical phase transition under shock initial conditions we show how the density fluctuation fields depend on the initial configuration

shocks in the asymmetric exclusion process in this paper we consider limit theorems for the asymmetric nearest neighbor exclusion process on the integers the initial distribution is a product measure with asymptotic density at and at earlier results described the limiting behavior in all cases except for 0 1 2 1 here we treat the exceptional case which is more delicate it corresponds to the one in which a shock wave occurs in an associated partial differential equation in the cases treated earlier the limit was an extremal invariant measure by contrast in the present case the limit is a mixture of two invariant measures our theorem resolves a conjecture made by the third author in 1975 7 the convergence proof is based on coupling and symmetry considerations

on a class of difference equations of monotone type of concern is the existence and uniqueness of the solution to a class of abstract second order difference equations they are the discrete version of some evolution equations which are intensely studied some asymptotic behavior results are established the periodic solutions are also investigated we use the theory of the maximal monotone operators in hilbert spaces an application to a partial differential equation is given

existence and equivalence with an optimization problem for some difference inclusions a discrete variant of a second order evolution equation is presented some existence theorems are given the equivalence with a minimization problem is established

a note on the strong convergence of solutions to a second order evolution equation abstract in this note with suitable assumptions on p t and r t we establish the strong convergence of solutions to the following nonlinear second order evolution equation p t u t r t u t a u t a e on r u 0 u 0 sup t 0 u t to a zero of a without assuming a 1 0 0 and determine the rate of convergence where a is a general maximal monotone operator we present also some applications of our result

second order fluctuations and current across characteristic for a one dimensional growth model of independent random walks fluctuations from a hydrodynamic limit of a one dimensional asymmetric system come at two levels on the central limit scale n 1 2 one sees initial fluctuations transported along characteristics and no dynamical noise the second order of fluctuations comes from the particle current across the characteristic for a system made up of independent random walks we show that the second order fluctuations appear at scale n 1 4 and converge to a certain self similar gaussian process if the system is in equilibrium this limiting process specializes to fractional brownian motion with hurst parameter 1 4 this contrasts with asymmetric exclusion and hammersley s process whose second order fluctuations appear at scale n 1 3 as has been discovered through related combinatorial growth models

numerical methods for the weakly compressible generalized langevin model in eulerian reference frame a well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations and to model non resolved scales by closures derived from transported probability density functions pdf for velocity fluctuations effective numerical methods for pdf transport employ the equivalence between the fokker planck equation for the pdf and a generalized langevin model glm and compute the pdf by transporting a set of sampling particles by glm pope 1985 1 the natural representation of glm is a system of stochastic differential equations in a lagrangian reference frame typically solved by particle methods a representation in a eulerian reference frame however has the potential to significantly reduce computational effort and to allow for the seamless integration into a eulerian frame numerical flow solver glm in a eulerian frame glmef formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by nakamura and yoshimori 2009 12 unlike the more common landau lifshitz navier stokes llns equations these equations are derived from the underdamped langevin equation and are not based on a local equilibrium assumption similarly to llns equations the numerical solution of glmef requires special considerations in this paper we investigate different numerical approaches to solving glmef with respect to the correct representation of stochastic properties of the solution we find that a discretely conservative staggered finite difference scheme adapted from a scheme originally proposed for turbulent incompressible flow in conjunction with a strongly stable for non stochastic pde runge kutta method performs better for glmef than schemes adopted from those proposed previously for the llns we show that equilibrium stochastic fluctuations are correctly reproduced

a new non linear two time level central leapfrog scheme in staggered conservation flux variables for fluctuating hydrodynamics equations with gpu implementation abstract for solving landau lifshitz navier stokes fluctuating hydrodynamics equations a two time level modification of the classical central leapfrog scheme with non linear flux correction is developed the new algorithm is simple for implementation and demonstrates high accuracy in satisfying the fluctuation dissipation theorem the numerical results for equilibrium and non equilibrium problems in one dimensional and three dimensional settings are compared with theoretical predictions the results from direct molecular dynamics simulations and also with those of several popular computational schemes in the literature because of simplicity and locality of the computational stencil the new algorithm can be efficiently implemented on the gpu which accelerates the calculation in comparison with a single cpu core computation by a factor of 300

a method for the 2 d quasi isometric regular grid generation a method for the generation of quasi isometric boundary fitted curvilinear coordinate systems for arbitrary domains is developed on the basis of the theory of conformal quasi conformal and quasi isometric mappings and results from the non euclidean geometry concerning surfaces of constant curvature the method as it is proposed has an advantage over similar methods developed earlier in that the number of unknown parameters to be found is decreased strict boundaries for parameters are found and a simple and efficient process of identification of an unknown parameter is given the reliability of the method is assured by an existence and uniqueness theorem for quasi isometric maps between physical regions and geodesic quadrangles on surfaces of constant curvature which are used to constrict quasi isometric grids in physical domains we formulate the riemannian metric consistent with this theorem which is available analytically illustrations of this technique are given for various domains

2d orthogonal grid generation with boundary point distribution control a numerical method for 2d orthogonal grid generation with control of the boundary point distribution is presented the method is based on the solution of a system of partial differential equations the grid cell aspect ratio the so called distortion function is calculated from its definition equation in the entire domain the method allows the specification of the boundary point distribution in all the boundaries and also the distance of the first grid node to the boundary the method is successfully applied to several geometries including geometries with grid singularities and grids around airfoils and cross sections of ship sterns

orthogonal grids around convex bodies using foliations a new technique for the construction of orthogonal grids around convex bodies is presented the method which is analytical or numerical depending on how the body boundary is expressed is based on the development of geometric foliations that follow a prescribed direction for instance the prevailing direction of flow around convex bodies of arbitrary shape the construction of these foliations is straightforward and does not require the solution of any system of algebraic or differential equations nor the use of iterative procedures the method is applicable both to two and three dimensional domains since it is based solely on the concept of local curtvature the lines or surfaces given by the foliations of first and second order together with the complementary orthogonal lines respectively define the orthogonal two or three dimensional grids

asymmetric attractive particle systems on z hydrodynamic limit for monotone initial profiles we extend previous results on the preservation of local equilibrium for one dimensional asymmetric attractive particle systems the hydrodynamic behavior is studied for general monotone initial profiles

a strong convergence theorem for solutions to a nonhomogeneous second order evolution equation abstract in this paper we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system u t c u t a u t f t a e t 0 u 0 u 0 sup t 0 u t to an element of a 1 0 with an exponential rate of convergence when f 0 where a is a general maximal monotone operator in a real hilbert space h c 0 is a real constant and f r h is a given function we show also that the curve u is almost nonexpansive and present some applications of our result

a fast algorithm for grid generation abstract the need for fast grid generation has become an important part of solving large complex computational fluid dynamic problems a new algorithm is developed for this purpose the two dimensional system of equations for coordinate generation includes a procedure to force the line spacing in the interior field to reflect the adjacent point distribution the coordinate generation equations in newton s iteration form are solved with a modified strongly implicit msi procedure the algorithm is applied to typical h o and c type grids and a practical problem configured as a forward facing cavity the grid generation equations were initialized with their laplacian counterpart all computations were performed on a microvax 3400 computer based on the numerical studies the proposed solution scheme is faster than the more common point sor and adi methods for large grid generation problems of practical interest the degree of computational saving however is highly problem dependent extensions of the solution scheme to problems involving three dimensions including surfaces in three dimensional space are described

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

limit processes for tasep with shocks and rarefaction fans we consider the totally asymmetric simple exclusion process tasep with two sided bernoulli initial condition i e with left density and right density we study the associated height function whose discrete gradient is given by the particle occurrences macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of we characterize the large time scaling limit of the multipoint fluctuations as a function of the densities and of the different macroscopic regions moreover using a slow decorrelation phenomena the results are extended from fixed time to the whole space time except along the some directions the characteristic solutions of the related burgers equation where the problem is still open

smoothness improvements of algebraic surface grid generation conclusion by adapting the grid with the three gridalgorithm we reduce not only the number of cells by almost 9 10 but also the cpu time by the same amount compared to single ne grid iteration and obtain a solutionclose to the ne grid solution the reduction in cpu time is due to both fewer iterations to convergenceand fewer cells there is a gain in cpu time on the adapted grid with multigrid iteration comparedto single griditeration thecpu time is about35 longer for the single grid

antishocks in the asep with open boundaries conditioned on low current we study the time evolution of the asep on a finite lattice with l sites and open boundaries conditioned on an atypically low current up to a finite time t by an exact computation we show that for a one parameter family of boundary densities and a special value of the conditioned current an initial product measure with an antishock at site k evolves into a convex combination of such antishocks at sites k the weights p k t k 0 are shown to be the transition probabilities of simple biased random walk with reflecting boundaries we compute explicitly these transition rates our result implies that the antishock remains microscopically stable under the locally conditioned dynamics

curvature flow and entropy conditions applied to grid generation we describe a numerical technique to generate logically rectangular body fitted interior and exterior grids the technique is based on solving a hamilton jacobi type equation for a propagating level set function using techniques borrowed from hyperbolic conservation laws coordinate grid lines are kept smooth through curvature terms which regularize the equation of motion and upwind difference schemes which satisfy the correct entropy conditions of front propagation the resulting algorithm can be used to generate two and three dimensional interior and exterior grids around reasonably complex bodies which may contain sharp corners and significant variations in curvature the technique may also be easily extended to problems of boundary fitted moving grids

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

hydrodynamical limit for the asymmetric simple exclusion process on demontre une loi forte des grands nombres pour le processus d exclusion simple asymetrique reechelonne

asymptotic behavior of bounded solutions to a class of second order nonhomogeneous difference equations of monotone type abstract as a continuation of our previous work in djafari rouhani and khatibzadeh 2008 1 we investigate the asymptotic behavior of solutions to the following system of second order nonhomogeneous difference equations u n 1 1 n u n n u n 1 c n a u n f n n 1 u 0 a h sup n 0 u n where a is a maximal monotone operator in a real hilbert space h c n and n are positive real sequences and f n is a sequence in h with suitable conditions on a and the sequences c n n and f n we show the weak or strong convergence of u n or its weighted average to an element of a 1 0 which is also the asymptotic center of the sequence u n implying therefore in particular that the existence of a solution u n implies that a 1 0 0 our results extend some previous results by apreutesei 2007 2003 2003 13 23 24 morosanu 1988 1979 4 20 and mitidieri and morosanu 1985 86 31 whose proofs use the assumption a 1 0 0 as well as the authors djafari rouhani and khatibzadeh 2008 1 as mentioned there in the section on future directions to the nonhomogeneous case with n 1 we also present some applications of our results to optimization

computational conformal mapping for surface grid generation the paper describes the development and application of a new approach for formulating an elliptic generation system on parametrically defined surfaces the present derivation of the surface equations proceeds in two steps first conformal mapping of smooth surfaces onto rectangular regions is utilized to derive a first order system of partial differential equations analogous to beltrami s system for quasi conformal mapping of planar regions second a general elliptic generation system for three dimensional surfaces including forcing functions is formulated based on beltrami s system and quasi conformal mapping the resulting elliptic system is solved using an iterative method on arbitrary surfaces represented analytically by rational b splines the overall effect of this approach is a reliable and versatile elliptic method for generating and improving surface grids examples will be presented to demonstrate the application of the method in constructing practical grids

a trotter kato type result for a second order difference inclusion in a hilbert space abstract a trotter kato type result is proved for a class of second order difference inclusions in a real hilbert space the equation contains a nonhomogeneous term f and is governed by a nonlinear operator a which is supposed to be maximal monotone and strongly monotone the associated boundary conditions are also of monotone type one shows that if a n is a sequence of operators which converges to a in the sense of resolvent and f n converges to f in a weighted l 2 space then under additional hypotheses the sequence of the solutions of the difference inclusion associated to a n and f n is uniformly convergent to the solution of the original problem

existence results for second order monotone differential inclusions on the positive half line abstract consider in a real hilbert space h the differential equation inclusion e p t u t q t u t a u t f t a e in 0 with the condition b u 0 x d a where a d a h h is a possibly set valued maximal monotone operator whose range contains 0 p q l 0 with ess inf p 0 and q l 1 0 more than four decades ago v barbu established the existence of a unique bounded solution to e b in the particular case p 1 q 0 and f 0 subsequently the existence and uniqueness of bounded solutions in the homogeneous case f 0 have been further investigated by h brezis 1972 n pavel 1976 l veron 1974 1976 and by e i poffald and s reich 1986 when a is an m accretive operator in a banach space the non homogeneous case has received less attention from this point of view in this paper we prove existence and uniqueness of bounded solutions to e b in the general case of non constant functions p q satisfying the mild conditions above thus compensating for the lack of existence theory for such kind of second order problems note that our results open up the possibility to apply lions method of artificial viscosity towards approximating the solutions of some nonlinear parabolic and hyperbolic problems as shown in the last section of the paper

elliptic grid generation based on laplace equations and algebraic transformations abstract an elliptic grid generation method is presented to generate boundary conforming grids in domains in 2d and 3d physical space and on minimal surfaces and parametrized surfaces in 3d physical space the elliptic grid generation method is based on the use of a composite mapping this composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation the elliptic transformation is based on the laplace equations for domains or on the laplace beltrami equations for surfaces the algebraic transformation maps the computational space one to one onto a parameter space the elliptic transformation maps the parameter space one to one onto the domains or surfaces the composition of these two mappings is a differentiable one to one mapping from computational space onto the domains or surfaces and has a nonvanishing jacobian this composite mapping defines the grid point distribution in the interior of the domains or surfaces for domains and minimal surfaces the composite mapping obeys a nonlinear elliptic poisson system with control functions completely defined by the algebraic transformation the solution of the poisson systems is obtained by picard iteration and black box multigrid solvers for parametrized curved surfaces it is not necessary to define and solve a nonlinear elliptic poisson system instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface

second order differential equations on half line associated with monotone operators abstract a boundary value problem for the second order differential equationpu ru au fon the half axis is studied here whereais a maximal monotone operator in a hilbert space we analyse the existence of uniqueness of the solution and the equivalence of the problem with an optimization problem in a special case

anomalous shock fluctuations in tasep and last passage percolation models we consider the totally asymmetric simple exclusion process with initial conditions and or jump rates such that shocks are generated if the initial condition is deterministic then the shock at time t will have a width of order t 1 3 we determine the law of particle positions in the large time limit around the shock in a few models in particular we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the airy 1 process the limiting distribution is a product of two distribution functions which is a consequence of the fact that at the shock two characteristics merge and of the slow decorrelation along the characteristics we show that the result generalizes to generic last passage percolation models

second class particles as microscopic characteristics in totally asymmetric nearest neighbor k exclusion processes summary we study aspects of the hydrodynamics of one dimensional totally asym metric k exclusion building on the hydrodynamic limit of seppalainen 1999 we prove that the weak solution chosen by the particle system is the unique one with maximal current past any fixed location a uniqueness result is needed because we can prove neither differentiability nor strict concavity of the flux function so we cannot use the lax oleinik formula or jump conditions to define entropy solutions next we prove laws of large numbers for a second class particle in k exclusion the macroscopic trajectories of second class particles are characteristics and shocks of the conservation law for the particle density in particular we extend tok exclusion ferrari s result that the second class particle follows a macroscopic shock in the rie mann solution the technical novelty of the proofs is a variational representation for the position of a second class particle in the context of the variational coupling method

variational curve and surface grid generation abstract variational algorithms that control the lengths of grid lines cell areas and the orthogonality of grid lines can be used for generating boundary conforming grids on surfaces additional geometric control is provided by using a reference grid while solution adaptivity is achieved by using weights in a typical application the reference grid can be used to produce an exponential compression of the grid at a boundary while the solution adaptive weights are used to make the grid spacing inversely proportional to the gradient when the gradient is large of some solution being computed on the grid the grid is adapted on both the interior and boundary of the surface the algorithm performs these tasks with exceptional precision as demonstrated in the examples presented here

new results on the asymptotic behavior of solutions to a class of second order nonhomogeneous difference equations abstract we investigate the asymptotic behavior of solutions to the following system of second order nonhomogeneous difference equation u n 1 1 n u n n u n 1 c n a u n f n n 1 u 0 x sup n 0 u n where a is a maximal monotone operator in a real hilbert space h c n and n are positive real sequences and f n is a sequence in h we show the weak and strong convergence of solutions and their weighted averages to an element of a 1 0 which is the asymptotic center of the sequence u n under appropriate assumptions on the sequences c n n and f n our results continue our previous work in djafari rouhani and khatibzadeh 2008 2010 30 31 by presenting some new results on the asymptotic behavior of solutions including in particular a completely new strong convergence result and extend some previous results by apreutesei 2003 27 28 morosanu 1979 21 and mitidieri and morosanu 1985 86 22 to the nonhomogeneous case and without assuming a to have a nonempty zero set