h2 boundedness of the pullback attractor for the non autonomous sir equations with diffusion abstract we prove some regularity results for the pullback attractor of a non autonomous sir model with diffusion in a bounded domain of r d where d 1 we show a regularity result for the unique solution of the problem we establish a general result about h 2 3 boundedness of invariant sets for the associate evolution process then as a consequence we deduce that the pullback attractor of the non autonomous system of sir equations with diffusion is bounded in h 2 3

ricci collineations of static spherically symmetric spacetimes the ricci collineations of static spherically symmetric spacetimes are classified and their relationship with isometries is discussed a general theorem about this relationship is stated and its extension to all spherically symmetric spacetimes is discussed

pullback attractors in v for non autonomous 2d navier stokes equations and their tempered behaviour abstract in this paper the asymptotic behaviour of the solutions to a non autonomous 2d navier stokes model is analyzed when the initial datum belongs to v for two frameworks the universe of fixed bounded sets and also for another universe given by a tempered condition the existence of pullback attractors in these different universes is established and thanks to regularity properties the relation between these several families of attractors and the corresponding in h is successfully studied finally two results about the tempered behaviour in v and h 2 2 of the pullback attractors when time goes to are obtained

classification of curvature collineations of plane symmetric static spacetimes a complete classification of curvature collineations of static plane symmetric spacetimes is obtained and then a comparison between isometries and ricci collineations of the corresponding metrics is given

classification of spherically symmetric static space times by their curvature collineations a complete classification of all spherically symmetric static space times according to their curvature collineations is presented and compared with ricci collineations of corresponding space times

upper semi continuity and regularity of random attractors on p times integrable spaces and applications abstract a sufficient condition for a family of random attractors to be upper semi continuous and regular is obtained when the state space is a p times integrable space with p 2 it is shown that both upper semi continuity and regularity under the topology of p norms do not rely on continuity convergence and absorption of the associated random dynamical systems in l p since the corresponding l 2 properties can offer all as an application of the abstract result it is shown that the family of random attractors for the stochastic reaction diffusion equations on a unbounded domain is upper semi continuous and regular at any point under the topology of p norms

killing vectors of static spherically symmetric metrics an error in a previous theorem j math phys 28 1019 1987 29 525 1988 is corrected and the theorem is extended

pullback attractors for asymptotically compact non autonomous dynamical systems abstract first we introduce the concept of pullback asymptotically compact non autonomous dynamical system as an extension of the similar concept in the autonomous framework our definition is different from that of asymptotic compactness already used in the theory of random and non autonomous dynamical systems as developed by crauel flandoli kloeden schmalfuss amongst others which means the existence of a random or time dependent family of compact attracting sets next we prove a result ensuring the existence of a pullback attractor for a non autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets this attractor is minimal and in most practical applications it is unique finally we illustrate the theory with a 2d navier stokes model in an unbounded domain

on the 3d kelvin voigt brinkman forchheimer equations in some unbounded domains abstract considered here is the first initial boundary value problem for the kelvin voigt brinkman forchheimer equations in three dimensional domains satisfying the poincare inequality the existence of a weak solution to the problem is proved by using the faedo galerkin method then we show the existence of a unique minimal pullback d attractor for the process associated to the problem with respect to a large class of non autonomous forcing terms finally the existence uniqueness and stability of a stationary solution is studied when the external force is time independent and small

flat surfaces in the hyperbolic 3 space in this paper we give a conformal representation of flat surfaces in the hyperbolic 3 space using the complex structure induced by its second fundamental form we also study some examples and the behaviour at infinity of complete flat ends

on the relation between two different concepts of pullback attractors for non autonomous dynamical systems abstract for an abstract dynamical system we establish under minimal assumptions the existence of d attractor i e a pullback attractor for a given class d of families of time varying subsets of the phase space we relate this concept with the usual attractor of fixed bounded sets pointing out its usefulness in order to ensure the existence of this last attractor in particular situations moreover we prove that under a simple assumption these two notions of attractors generate in fact the same object this is then applied to a navier stokes model improving some previous results on attractor theory

complete flat surfaces with two isolated singularities in hyperbolic 3 space abstract we construct examples of flat surfaces in h 3 which are graphs over a two punctured horosphere and classify complete embedded flat surfaces in h 3 with only one end and at most two isolated singularities

pullback attractors for the non autonomous reaction diffusion equations in rn in this paper we prove the existence of the pullback attractors in l2 rn lp rn and h1 rn for a nonlinear reaction diffusion equation in unbounded domains in which the nonlinearity f satisfies the polynomial growth of arbitrary order p 1 p 2 and the external forcing g lloc2 r l2 rn only subjects to the weaker integrability condition te s g s 22ds in this paper we prove the existence of the pullback attractors in l2 rn lp rn and h1 rn for a nonlinear reaction diffusion equation in unbounded domains in which the nonlinearity f satisfies the polynomial growth of arbitrary order p 1 p 2 and the external forcing g lloc2 r l2 rn only subjects to the weaker integrability condition te s g s 22ds

ricci collineation vectors in fluid space times the properties of fluid space times that admit a ricci collineation vector rcv parallel to the fluid unit four velocity vector ua are briefly reviewed these properties are expressed in terms of the kinematic quantities of the timelike congruence generated by ua the cubic equation derived by oliver and davis ann inst henri poincare 30 339 1979 for the equation of state p p of a perfect fluid space time that admits an rcv which does not degenerate to a killing vector is solved for physically realistic fluids necessary and sufficient conditions for a fluid space time to admit a spacelike rcv parallel to a unit vector na orthogonal to ua are derived in terms of the expansion shear and rotation of the spacelike congruence generated by na perfect fluid space times are studied in detail and analogues of the results for timelike rcvs parallel to ua are obtained properties of imperfect fluid space times for which the energy flux vector qa vanishes and na is a spacelike eigenvector of the aniso

h2 boundedness of the pullback attractor for a non autonomous reaction diffusion equation abstract we prove some regularity results for the pullback attractor of a reaction diffusion model first we establish a general result about h 2 boundedness of invariant sets for an evolution process then as a consequence we deduce that the pullback attractor of a non autonomous reaction diffusion equation is bounded not only in l 2 h 0 1 but also in h 2

the classification of static plane symmetric space times according to their ricci collineations static plane symmetric space times are classified according to their ricci collineations rcs their relation with isometries of the space times is established unlike the spherically symmetric space times some metrics are found for a nondegenerate ricci tensor which have more rcs than isometries

ribaucour transformations for flat surfaces in the hyperbolic 3 space abstract we consider ribaucour transformations for flat surfaces in the hyperbolic 3 space h 3 we show that such transformations produce complete embedded ends of horosphere type and curves of singularities which generically are cuspidal edges moreover we prove that these ends and curves of singularities do not intersect we apply ribaucour transformations to rotational flat surfaces in h 3 providing new families of explicitly given flat surfaces h 3 which are determined by several parameters for special choices of the parameters we get surfaces that are periodic in one variable and surfaces with any even number or an infinite number of embedded ends of horosphere type

collineations of godel type space times ricci collineations for godel type space times are studied the members of this family of metrics admitting these symmetries are identified it is shown that these space times do not admit homothetic vector fields also the unique affine collineation associated to godel type space times is exhibited

surfaces of constant curvature in r3 with isolated singularities abstract we prove that finite area isolated singularities of surfaces with constant positive curvature k 0 in r 3 are removable singularities branch points or immersed conical singularities we describe the space of immersed conical singularities of such surfaces in terms of the class of real analytic closed locally strictly convex curves in s 2 with admissible cusp singularities characterizing when the singularity is actually embedded in the global setting we describe the space of peaked spheres in r 3 i e compact convex surfaces of constant curvature k 0 with a finite number of singularities and give applications to harmonic maps and constant mean curvature surfaces

continuity and pullback attractors for a non autonomous reaction diffusion equation in r n in this paper we study the dynamics of a non autonomous reaction diffusion equation in r n with the nonlinearity f satisfying the polynomial growth of arbitrary order p 1 p 2 firstly we prove the existence of the pullback d attractor in l 2 r n secondly we use a scheme to establish some new estimates higher order integrability of the difference of the solutions near the initial time instead of using the usual estimates about higher regularities and higher order integrability of solutions thirdly we verify that the usual l 2 r n l 2 r n pullback d attractor indeed can pullback attract the d class in l 2 norm for any 0 and h 1 norm and the solutions of the equation in h 1 r n are continuous with respect to initial data finally we obtain the pullback d attractor in l p r n and h 1 r n as an application of the higher order integrability and the continuity respectively

attractors for 2d navier stokes models with delays abstract the existence of an attractor for a 2d navier stokes system with delay is proved the theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous however on some occasions the attractors may attract not only in the pullback sense but in the forward one as well also this formulation allows to treat in a unified way terms containing various classes of delay features constant variable distributed delays etc as a consequence some results for the autonomous model are deduced as particular cases of our general formulation

collineations of the ricci tensor ricci collineations for the ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of rab r such that rab 0 for a b it turns out that the only collineations admitted by this tensor can be ten six or four and there does not appear any case in between

h2 boundedness of the pullback attractors for non autonomous 2d navier stokes equations in bounded domains abstract we prove some regularity results for the pullback attractors of a non autonomous 2d navier stokes model in a bounded domain of r 2 we establish a general result about h 2 2 v boundedness of invariant sets for the associate evolution process then as a consequence we deduce that under adequate assumptions the pullback attractors of the non autonomous 2d navier stokes equations are bounded not only in v but also in h 2 2

asymptotic behaviour of nonautonomous difference inclusions abstract nonautonomous difference inclusions are formulated as difference inclusion cocycles which generalize set valued semigroups corresponding to autonomous difference inclusions and the existence of a difference inclusion cocycle attractor is established under the assumption of upper semi continuity of the cocycle mappings if the difference inclusion cocycle has an absorbing set several illustrative examples are provided

the global attractor for the 2d navier stokes flow on some unbounded domains we extend previous results on the existence of the global attractor for the 2d navier stokes equations on some unbounded domains in the sense that the forcing term need not lie in any weighted space nor is the boundary of the domain required to be smooth the existence of the global attractor is obtained on arbitrary open sets such that the poincare inequality holds and for forces in the natural dual space v the proof is based on the energy equation and the concept of asymptotic compactness an estimate of the hausdorff and fractal dimensions of the attractor is also given

on the generalized weyl problem for flat metrics in the hyperbolic 3 space abstract the paper deals with the study of complete embedded flat surfaces in h 3 with a finite number of isolated singularities we give a detailed information about its topology conformal type and metric properties we show how to solve the generalized weyl s problem of realizing isometrically any complete flat metric with euclidean singularities in h 3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities

long time behavior of a non autonomous parabolic equation with nonlocal diffusion and sublinear terms abstract this paper is devoted to study the asymptotic behavior of a time dependent parabolic equation with nonlocal diffusion and nonlinear terms with sublinear growth namely we extend some previous results from the literature obtaining existence uniqueness and continuity results analyzing the stationary problem and decay of the solutions of the evolutionary problem and finally under more general assumptions ensuring the existence of pullback attractors for the associated dynamical system in both l 2 and h 1 norms relationships among these objects are established using regularizing properties of the equation