on the asymptotic behavior for a certain nonlinear evolution equation let x be a real banach space we shall say that an operator a with domain d a and range r a in x is accretive if lx x2 11 0 and yi e axi i 1 2 and that a satisfies the range condition if r z i 1 d a the closure of d a for all a 0 where 1 denotes the identity let g 0 co 0 co be a nonincreasing continuous function such that lim r13 g t 0 let x e x and consider the following initial value problem

exact solutions to nonlinear nonautonomous space fractional diffusion equations with absorption we analyze a nonlinear fractional diffusion equation with absorption by employing fractional spatial derivatives and obtain some more exact classes of solutions in particular the diffusion equation employed here extends some known diffusion equations such as the porous medium equation and the thin film equation we also discuss some implications by considering a diffusion coefficient d x t d t x theta theta in r and a drift force f k 1 t x k alpha x x alpha 1 in both situations we relate our solutions to those obtained within the maximum entropy principle by using the tsallis entropy

the q gamma and q q polygamma functions of tsallis statistics abstract an axiomatic definition is given for the q gamma function q x q r q 0 x r of tsallis non extensive statistical physics the continuous analogue of the q factorial of suyari h suyari physica a 368 1 2006 63 and the q analogue of the gamma function x of euler and gauss a working definition in closed form based on the hurwitz and riemann zeta functions including their analytic continuations is shown to satisfy this definition several relations involving the q gamma and other functions are obtained the q q polygamma functions q q m x m n defined by successive derivatives of ln q q x where ln q a 1 q 1 a 1 q 1 a 0 is the q logarithmic function are also reported the new functions are used to calculate the inferred probabilities and multipliers for tsallis systems with finite numbers of particles n

asymptotic behavior of solutions to nonlinear volterra integral equations in section 2 we establish the existence of solutions to 1 1 and to related equations theorems 2 1 and 2 3 in contrast with previous papers e g 7 we do not assume that a is m accretive instead we require a to satisfy a weaker cone condition certain other facts are also included in this section throughout this paper we also assume that b is completely positive 6 in the third section we present two mean ergodic theorems for the solutions of 1 1 in hilbert space the first theorem theorem 3 1 deals with weak almost convergence and the second theorem 3 4 with strong almost convergence these results improve upon those of 1 and include the known results for nonlinear semigroups 191 it is important to establish almost convergence because it then follows that the solution is summed by every strongly regular kernel corollaries 3 3 and 3 5 a weak convergence criterion corollary 3 2 is also obtained if the banach space x is reflexive and strictly convex and 0 e r a then

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

nonlinear fokker planck equations and generalized entropies abstract we consider maximum entropy solutions to nonlinear fokker planck equations within general thermostatistical formalisms we show that the family of generalized nonextensive entropies introduced by tsallis is the only one that has an associated family of nonlinear fokker planck equations endowed with time dependent maxent solutions of a generalized gaussian type consequently the natural association that arises between tsallis thermostatistical formalism and special families of nonlinear fokker planck equations is not a universal feature of general thermostatistical formalisms but a particular feature of the tsallis one

on a general link between anomalous diffusion and nonextensivity stochastic processes of systems with composable entropy measures are studied the processes are described by fokker planck equations which are nonlinear with respect to their probability densities and whose diffusion coefficients are derived from the entropy measures in questions in nonextensive extensive systems anomalous normal diffusion is found

nonlinear diffusion equation and nonlinear external force exact solution the solutions of the nonlinear diffusion equation t r1 nd r rn 1 r r r1 n r rn 1f are investigated by considering the presence of an external force f which exhibits an explicit dependence on the distribution first the stationary case is considered after that the dynamical case i e the case dependent on time the stationary solution is obtained by considering the external force f r f1 r f2 r r 1 and the result found is related to the distributions which emerge from the tsallis statistics or the boltzmann gibbs statistics the dynamical solution is investigated by considering the external force f r t k t r k r1 r t 1 and related to the levy distributions in the asymptotic limit in both cases the solutions are expressed in terms of the q exponentials and the q logarithmics functions which emerge from the tsallis formalism

n dimensional nonlinear fokker planck equation with time dependent coefficients an n dimensional nonlinear fokker planck equation is investigated here by considering the time dependence of the coefficients where drift controlled and source terms are present we exhibit the exact solution based on the generalized gaussian function related to the tsallis statistics furthermore we show that a rich class of diffusive processes including normal and anomalous ones can be obtained by changing the time dependence of the coefficients

on the unbounded behavior for some non autonomous systems in banach spaces abstract by modifying our previous methods 1992 j nonlinear anal tma 19 741 751 1993 proc amer math soc 117 951 956 and by using the notion of integral solution introduced by ph benilan 1972 equations d evolution dans un espace de banach quelconque et applications thesis universite paris xi orsay we study the asymptotic behaviour of unbounded trajectories for the quasi autonomous dissipative system du dt au where x is a real banach space a an accretive possibly multivalued operator in x x and l p 0 x for some x and 1 p

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

a criterion of closedness of an attainable set of a delay system this paper deals with the problem of closedness of an attainable set of a delay system in the state space w21 we give a necessary and sufficient condition of closedness expressed in terms of the transfer matrix of the system

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

a nonextensive maximum entropy approach to a family of nonlinear reaction diffusion equations we consider a monoparametric family of reaction diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time dependent particular solutions of the tsallis maximum entropy maxent form the evolution of these solutions is governed by a system of three coupled nonlinear ordinary differential equations that are integrated numerically a simple population dynamics interpretation provides a qualitative understanding of the behaviour of the q maxent solutions when the reaction term vanishes the time dependent distributions studied here reduce to the previously known tsallis maxent solutions for the nonlinear diffusion equation

the asymptotics of nonexpansive iterations abstract let d be a closed subset of a banach space x and t d d a nonexpansive mapping conditions are given on the space x for t to satisfy the following property of ergodic type t n x n converges either weakly or strongly to a vector v rather unexpectedly d is not assumed to be convex nor is i t assumed to satisfy any range condition in addition it is shown that v is the unique point of least norm in the closure of r i t if and only if i t satisfies a certain range condition at infinity several interesting applications to accretive operator and nonlinear semigroup theory are also included

nonlinear fractional diffusion equation exact results the nonlinear fractional diffusion equation t r1 d r rd 1d r t r r1 d r rd 1f r t t is studied by considering the diffusion coefficient d r t d t r and the external force f r t k1 t r k r in addition a rich class of diffusive processes including normal and anomalous ones is obtained from the study present in this work

nonlinear equation for anomalous diffusion unified power law and stretched exponential exact solution the nonlinear diffusion equation ensuremath partial ensuremath rho ensuremath partial t d stackrel ifmmode tilde else fi ensuremath delta ensuremath rho ensuremath nu is analyzed here where stackrel ifmmode tilde else fi ensuremath delta ensuremath equiv 1 r d ensuremath 1 ensuremath partial ensuremath partial r r d ensuremath 1 ensuremath ensuremath theta ensuremath partial ensuremath partial r and d ensuremath theta and ensuremath nu are real parameters this equation unifies the anomalous diffusion equation on fractals ensuremath nu 1 and the spherical anomalous diffusion for porous media ensuremath theta 0 an exact point source solution is obtained enabling us to describe a large class of subdiffusion ensuremath theta g 1 ensuremath ensuremath nu d normal diffusion ensuremath theta 1 ensuremath ensuremath nu d and superdiffusion ensuremath theta l 1 ensuremath ensuremath nu d furthermore a thermostatistical basis for this solution is given from the maximum entropic principle applied to the tsallis entropy

an algebraic characterization of closed small attainability subspaces of delay systems if small attainability subspaces of linear time delay systems are closed in a certain sobolev space the existence of lagrange multipliers for optimal control to small solutions is guaranteed this paper characterizes the required closedness property using an algebraic approach due to b jakubczyk as a main result it turns out that closedness is in an algebraic sense generic in the variety of system matrices a0 a1 b0 with rank a1 not greater than the dimension of the control space this is in contrast to known results on closedness of attainability subspaces playing an analogous role for optimal control to fixed final states instead of small solutions

optimal control of linear retarded systems to small solutions this paper deals with necessary optimality conditions for control of general linear retarded systems to small solutions here the final states at time t are required to generate small solutions of the uncontrolled system vanishing after t h where 0 is fixed this generalizes the fixed final state problem where 0 and for h includes problems with fixed reduced final state fx t where f is the structural operator of the delay system necessary optimality conditions in the form of a maximum principle are valid if a certain space called the small attainability sub space is closed in a sobolev space a sufficient criterion for this closedness property is indicated finally an example is discussed where the maximum principle for the fixed final state problem is not valid while the new problem with h can be solved by an application of the obtained results

quasi stationary states of the nrt nonlinear schrodinger equation abstract with regards to the nonlinear schrodinger equation recently advanced by nobre rego monteiro and tsallis nrt based on tsallis q thermo statistical formalism we investigate the existence and properties of its quasi stationary solutions which have the time and space dependences separated in a q deformed fashion one recovers the normal factorization into purely spatial and purely temporal factors corresponding to the standard linear schrodinger equation when the deformation vanishes q 1 we discuss various specific examples of exact quasi stationary solutions of the nrt equation in particular we obtain a quasi stationary solution for the moshinsky model providing the first example of an exact solution of the nrt equation for a system of interacting particles

asymptotic properties of some non autonomous systems in banach spaces abstract let x be a reflexive banach space we introduce the notion of weakly almost nonexpansive sequences x n n 0 in x and study their asymptotic behavior by showing that the nonempty weak limit set of the sequence x n n n 1 always lies on a convex subset of a sphere centered at the origin of radius d lim n x n n subsequently we apply our results to study the asymptotic properties of unbounded trajectories for the quasi autonomous dissipative system d u d t a u f where a is an accretive possibly multivalued operator in x x and f f l p 0 x for some f x and 1 p these results extend recent results of j s jung and j s park j s jung j s park asymptotic behavior of nonexpansive sequences and mean points proc amer math soc 124 1996 475 480 and j s jung j s park and e h park j s jung j s park e h park asymptotic behaviour of generalized almost nonexpansive sequences and applications proc nonlinear funct anal 1 1996 65 79 as well as our results cited below containing previous results by several authors

existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions abstract this paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in banach spaces first using the approach of geometry of banach space hausdorff metric the measure of noncompactness and fixed point existence results are obtained we have removed from previous papers the crucial restriction on the semigroup then we establish the asymptotic properties of integral solutions when t finally for illustration a partial differential equation is worked out

asymptotic properties of nonexpansive iterations in reflexive spaces abstract let x be a reflexive banach space and xn n 0 a nonexpansive resp firmly nonexpansive sequence in x it is shown that the set of weak limit points of the sequence xn n n 1 resp xn 1 xn n 0 always lies on a convex subset of a sphere centered at the origin of radius d limn xn n this fact quickly yields previous results of b djafari rouhani as well as recent results of j s jung and j s park potential applications are also discussed