a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

chemotaxis with logistic source very weak global solutions and their boundedness properties abstract we consider the chemotaxis system u t u u v g u x t 0 0 v v u x t 0 in a smooth bounded domain r n where 0 and g generalizes the logistic function g u a u b u with 1 a 0 and b 0 a concept of very weak solutions is introduced and global existence of such solutions for any nonnegative initial data u 0 l 1 is proved under the assumption that 2 1 n moreover boundedness properties of the constructed solutions are studied inter alia it is shown that if b is sufficiently large and u 0 l has small norm in l for some n 2 then the solution is globally bounded finally in the case that additionally n 2 holds a bounded set in l can be found which eventually attracts very weak solutions emanating from arbitrary l 1 initial data the paper closes with numerical experiments that illustrate some of the theoretically established results

persistence of mass in a chemotaxis system with logistic source this paper studies the dynamical properties of the chemotaxis system ut u u v ru u2 x t 0 vt v v u x t 0 under homogeneous neumann boundary conditions in bounded convex domains rn n 1 with positive constants r and numerical simulations but also some rigorous evidence have shown that depending on the relative size of r and in comparison to the well understood case when 0 this problem may exhibit quite a complex solution behavior including unexpected effects such as asymptotic decay of the quantity u within large subdomains of the present work indicates that any such extinction phenomenon if occurring at all necessarily must be of spatially local nature whereas the population as a whole always persists more precisely it is shown that for any nonnegative global classical solution u v of with u 0 one can find m 0 such that u x t dx m for all t 0 the proof is based on an in this context apparently novel analysis of the functional ln u deriving a lower bound for this quantity along a suitable sequence of times by appropriately exploiting a differential inequality for a suitable linear combination of ln u u and v2

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

very weak global solutions to a parabolic parabolic chemotaxis system with logistic source abstract in this paper we study this chemotaxis system u t u u v g u x t 0 v t v v u x t 0 defined in a convex smooth and bounded domain of r n with n 1 and endowed with homogeneous neumann boundary conditions being 0 and g a sort of logistic function obeying growth technical restrictions specifically once an appropriate definition of very weak solution is given our main result deals with the global existence of such solutions for any nonnegative initial data u 0 v 0 c 0 c 2 and under zero flux boundary condition on v 0

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

a new result for global existence and boundedness of solutions to a parabolic parabolic keller segel system with logistic source abstract we consider the following fully parabolic keller segel system with logistic source ks u t u u v a u u 2 x t 0 v t v v u x t 0 over a bounded domain r n n 1 with smooth boundary the parameters a r 0 0 it is proved that if 0 then ks admits a global weak solution while if n 2 n c n 2 1 1 n 2 1 then ks possesses a global classical solution which is bounded where c n 2 1 1 n 2 1 is a positive constant which is corresponding to the maximal sobolev regularity apart from this we also show that if a 0 and n 2 n c n 2 1 1 n 2 1 then both u t and v t decay to zero with respect to the norm in l as t

a new result for boundedness in the quasilinear parabolic parabolic keller segel model with logistic source abstract the current paper considers the boundedness of solutions to the following quasilinear keller segel model with logistic source ks u t d u u u v u u 2 x t 0 v t v u v x t 0 d u u u v v 0 x t 0 u x 0 u 0 x v x 0 v 0 x x where r n n 1 is a bounded domain with smooth boundary 0 and 0 one novelty of this paper is that we find a new a priori estimate u max 1 0 max 1 0 e x t d x so that we develop new l p estimate techniques and thereby obtain the boundedness results where c g n and 0 0 are the constants which are corresponding to the gagliardo nirenberg inequality see lemma 2 2 and the maximal sobolev regularity see lemma 2 3 to our best knowledge this seems to be the first rigorous mathematical result which indicates the relationship between m and that yields the boundedness of the solutions where m is the exponent of diffusion term d u the above mentioned results have significantly improved and extended previous results of several authors

stratified partial likelihood estimation when multiple durations are generated by a single unit they may be related in a way that is not fully captured by the regressors the omitted unit specific variables might vary over the durations they might also be correlated with the variables in the regression component we propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit specific effects data from malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables and that failure to control for unobserved heterogeneity seriously biases the parameter estimates

boundedness and decay behavior in a higher dimensional quasilinear chemotaxis system with nonlinear logistic source this paper is concerned with a class of quasilinear chemotaxis systems generalizing the prototype 0 1 ut um uv uur x t 0 vt vv u x t 0 u v 0 x t 0 u x 0 u0 x v x 0 v0 x x in a smooth bounded domain rn n2 with parameters m r1 and 0 the pde system in 0 1 is used in mathematical biology to model the mechanism of chemotaxis that is the movement of cells in response to the presence of a chemical signal substance which is in homogeneously distributed in space it is shown that if m 22nif11 n 22r n 2ifn 22rn 2n 1ifr n 22 and the nonnegative initial data u0 v0 c w1 0 then 0 1 possesses at least one global bounded weak solution apart from this it is proved that if 0 then both u t and v t decay to zero with respect to the norm in l as t

flood frequency analysis using the cox regression model procedures for incorporating time varying exogenous information into flood frequency analyses are developed using the cox regression model for counting processes in this statistical model the probability of occurrence of a flood peak in a short interval t t dt depends in an explicit manner on the values at t of k covariate processes z1 zk specifically letting dn t be 1 if a flood peak occurs in t t dt and 0 otherwise dn t a t exp j 1kbjzj t dm t where a the baseline intensity is an unknown function b is a vector of unknown regression parameters and the error dm t is conditionally orthogonal to the past history two applications assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time varying flood frequency estimates are considered

blow up in a higher dimensional chemotaxis system despite logistic growth restriction abstract we study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype u t u u v u u x t 0 0 v m t u x t 0 in a ball r n with parameters 0 0 0 and 1 and m t 1 u x t d x it is shown that when n 5 and 3 2 1 2 n 2 then there exist initial data such that the smooth local in time solution of blows up in finite time this indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse as is known to occur in the corresponding system without any proliferation

boundedness and finite time collapse in a chemotaxis system with volume filling effect abstract we consider the elliptic parabolic pde system u t u u u v x t 0 0 v m u x t 0 with nonnegative initial data u 0 having mean value m under homogeneous neumann boundary conditions in a smooth bounded domain r n the nonlinearities and are supposed to generalize the prototypes u u 1 p u u u 1 q 1 with p 0 and q r problems of this type arise as simplified models in the theoretical description of chemotaxis phenomena under the influence of the volume filling effect as introduced by painter and hillen k j painter t hillen volume filling and quorum sensing in models for chemosensitive movement can appl math q 10 2002 501 543 it is proved that if p q 2 n then all solutions are global in time and bounded whereas if p q 2 n q 0 and is a ball then there exist solutions that become unbounded in finite time the former result is consistent with the aggregation inhibiting effect of the volume filling mechanism the latter however is shown to imply that if the space dimension is at least three then chemotactic collapse may occur despite the presence of some nonlinearities that supposedly model a volume filling effect in the sense of painter and hillen

pointwise persistence in full chemotaxis models with logistic source on bounded heterogeneous environments abstract the current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains we first prove the global existence and boundedness of nonnegative classical solutions under some conditions on the coefficients in the models next under the same conditions on the coefficients we show that pointwise persistence occurs that is any globally defined positive solution is bounded below by a positive constant independent of its initial condition when the time is large enough it should be pointed out that in 21 the authors established the persistence of mass for globally defined positive solutions which indicates that any extinction phenomenon if occurring at all necessarily must be spatially local in nature whereas the population as a whole always persists the pointwise persistence proved in the current paper implies that not only the population as a whole persists but also it persists at any location eventually it also implies the existence of strictly positive entire solutions

finite time blowup and global in time unbounded solutions to a parabolic parabolic quasilinear keller segel system in higher dimensions abstract in this paper we consider quasilinear keller segel type systems of two kinds in higher dimensions in the case of a nonlinear diffusion system we prove an optimal with respect to possible nonlinear diffusions generating explosion in finite time of solutions finite time blowup result in the case of a cross diffusion system we give results which are optimal provided one assumes some proper non decay of a nonlinear chemical sensitivity moreover we show that once we do not assume the above mentioned non decay our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross diffusion terms to this end we provide an example interesting by itself of global in time unbounded solutions to the nonlinear cross diffusion keller segel system with chemical sensitivity decaying fast enough in a range of parameters in which there is a finite time blowup result in a corresponding case without nonlinear cross diffusion

the l 1 method for robust nonparametric regression abstract consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy tailed error distribution the two standard approaches to such a problem are each flawed robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods which are not resistant against outliers existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares neither of these two approaches combines computational ease with asymptotic theoretical results furthermore application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable in this article a new hybrid method is propose

boundedness in a quasilinear parabolic parabolic keller segel system with logistic source abstract we consider a quasilinear parabolic parabolic keller segel system involving a source term of logistic type 0 1 u t u u u v g u x t 0 t v t v v u x t 0 t with nonnegative initial data under neumann boundary condition in a smooth bounded domain r n n 1 here and are supposed to be smooth positive functions satisfying c 1 s p and c 1 s q s c 2 s q when s s 0 with some s 0 1 and we assume that g is smooth on 0 fulfilling g 0 0 and g s a s s 2 for all s 0 with constants a 0 and 0 within this framework it is proved that whenever q 1 for any sufficiently smooth initial data there exists a unique classical solution which is global in time and bounded our result is independent of p

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

boundedness and global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with nonlinear logistic source abstract this paper deals with a fully parabolic chemotaxis system with nonlinear logistic source 0 1 u t u u v u 1 u r 1 v t v v u under homogeneous neumann boundary conditions in a smooth bounded convex domain r n with parameters 0 r 2 it is shown that if r 2 or r 2 and n 4 then for all sufficiently smooth initial data the associated initial boundary value problem 0 1 possesses a unique global in time classical solution that is bounded in 0 which satisfies lim sup t u t l max t 0 n 4 t 2 r t t r min r 1 2 moreover with the assumption u 0 0 and appropriate growth assumptions the globally asymptotical stability of 1 1 r 1 1 1 r 1 is established

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

tightening the uncertainty principle for stochastic currents we connect two recent advances in the stochastic analysis of nonequilibrium systems the loose uncertainty principle for the currents which states that statistical errors are bounded by thermodynamic dissipation and the analysis of thermodynamic consistency of the currents in the light of symmetries employing the large deviation techniques presented by gingrich et al phys rev lett 116 120601 2016 prltao0031 900710 1103 physrevlett 116 120601 and pietzonka barato and seifert phys rev e 93 052145 2016 2470 004510 1103 physreve 93 052145 we provide a short proof of the loose uncertainty principle and prove a tighter uncertainty relation for a class of thermodynamically consistent currents j our bound involves a measure of partial entropy production that we interpret as the least amount of entropy that a system sustaining current j can possibly produce at a given steady state we provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal and finally we argue that the relationship for the fano factor of the entropy production rate var mean 2 is the most significant realization of the loose bound we base our analysis both on the formalism of diffusions and of markov jump processes in the light of schnakenberg s cycle analysis

boundedness and global existence in the higher dimensional parabolic parabolic chemotaxis system with without growth source abstract in this paper we are concerned with a general class of quasilinear parabolic parabolic chemotaxis systems with without growth source under homogeneous neumann boundary conditions in a smooth bounded domain r n with n 2 it is recently known that blowup is possible even in the presence of superlinear growth restrictions here we derive new and interesting characterizations on the growth versus the boundedness we show that the hard task of proving the l boundedness of the cell density can be reduced to proving its l r boundedness in other words we show that the l r boundedness of the cell density can successfully guarantee its l boundedness and hence its global boundedness where r n or n 2 depending on whether the growth restriction is essentially linear including no growth or superlinear hence a blowup solution also blows up in l p norm for any suitably large p more detailed information on how the growth source affects the boundedness of the solution is derived these results reveal deep understandings of blowup mechanism for chemotaxis models then we use these criteria to establish uniform boundedness and hence global existence of the underlying models logistic source in 2 d cubic source as initially proposed by mimura and tsujikawa in 3 d n 1 st source in n d with n 4 as a consequence in a chemotaxis growth model blowup is impossible if the growth effect is suitably strong finally we underline that our results remove the commonly assumed convexity on the domain

global weak solutions in a three dimensional keller segel navier stokes system with nonlinear diffusion abstract the coupled quasilinear keller segel navier stokes system ksnf n t u n n m n c x t 0 c t u c c c n x t 0 u t u u p u n x t 0 u 0 x t 0 is considered under neumann boundary conditions for n and c and no slip boundary conditions for u in three dimensional bounded domains r 3 with smooth boundary where m 0 r are given constants w 1 if m 2 then for all reasonably regular initial data a corresponding initial boundary value problem for ksnf possesses a globally defined weak solution

an optimal result for global existence and boundedness in a three dimensional keller segel stokes system with nonlinear diffusion abstract this paper investigates the following keller segel stokes system with nonlinear diffusion k s f n t u n n m n c x t 0 c t u c c c n x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous boundary conditions of neumann type for n and c and of dirichlet type for u in a three dimensional bounded domains r 3 with smooth boundary where w 2 m 0 it is proved that if m 4 3 then for any sufficiently regular nonnegative initial data there exists at least one global boundedness solution for system k s f which in view of the known results for the fluid free system mentioned below see introduction is an optimal restriction on m

on a quasilinear parabolic elliptic chemotaxis system with logistic source abstract this paper deals with a quasilinear parabolic elliptic chemotaxis system with logistic source under homogeneous neumann boundary conditions in a smooth bounded domain for the case of positive diffusion function it is shown that the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded moreover if the diffusion function is zero at some point or a positive diffusion function and the logistic damping effect is rather mild we proved that the weak solutions are global existence finally it is asserted that the solutions approach constant equilibria in the large time for a specific case of the logistic source

the asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time the log rank test derived by mantel 1966 and peto 1972 is a special case of the efficient scores test for the proportional hazards model it is used frequently in the analysis of survival duration in clinical trials where patients entering the study are assigned at random to different treatments and are followed until they either fail or the study is terminated most survival studies are designed so that the log rank test is calculated at the termination of the study however it is not unusual for the investigator to monitor the experiment periodically it would be very useful to know the joint distribution of the test statistic at different points in time in order to adjust for the effect of repeated significance testing although the joint distribution has not been derived previously sequential procedures for the analysis of survival data in clinical trials have been given by several authors including armitage 1975 pp 140 6 jones whitehead 1979 and nagelkerke hart 1980 in this paper we establish the asymptotic joint distribution of the more general efficient scores test for the proportional hazards model calculated at different points in time and indicate how this can be used for repeated significance testing

boundedness in a quasilinear parabolic parabolic keller segel system with subcritical sensitivity abstract we consider the quasilinear parabolic parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a convex smooth bounded domain r n with n 1 it is proved that if s u d u c u with 2 n and some constant c 0 for all u 1 then the classical solutions to the above system are uniformly in time bounded provided that d u satisfies some technical conditions such as algebraic upper and lower growth resp decay estimates as u this boundedness result is optimal according to a recent result by the second author winkler 2010 27 which says that if s u d u c u for u 1 with c 0 and some 2 n n 2 then for each mass m 0 there exist blow up solutions with mass u 0 m in addition this paper also proves a general boundedness result for quasilinear non uniformly parabolic equations by modifying the iterative technique of moser alikakos alikakos 1979 1

competing risks regression for stratified data for competing risks data the fine gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function however in many important applications proportional hazards may not be satisfied including multicenter clinical trials where the baseline subdistribution hazards may not be common due to varying patient populations in this article we consider a stratified competing risks regression to allow the baseline hazard to vary across levels of the stratification covariate according to the relative size of the number of strata and strata sizes two stratification regimes are considered using partial likelihood and weighting techniques we obtain consistent estimators of regression parameters the corresponding asymptotic properties and resulting inferences are provided for the two regimes separately data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified fine gray model

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations abstract we prove interior and boundary holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t div u m 1 du p 2 du

global existence and asymptotic behavior of the fractional chemotaxis system with signal dependent sensitivity abstract in this paper we study a fractional chemotaxis model with signal dependent sensitivity and the source term which involves two parabolic equations with fractional diffusions we develop a suitable mathematical framework for a unified treatment of the existence and decay estimates based on an appropriate functional space we show the existence uniqueness and temporal decay of the global classical solutions to the problem simultaneously under the smallness initial assumptions

eventual smoothness and asymptotics in a three dimensional chemotaxis system with logistic source abstract we prove existence of global weak solutions to the chemotaxis system u t u u v u u 2 v t v v u under homogeneous neumann boundary conditions in a smooth bounded convex domain r n for arbitrarily small values of 0 additionally we show that in the three dimensional setting after some time these solutions become classical solutions provided that is not too large in this case we also consider their large time behaviour we prove decay if 0 and the existence of an absorbing set if 0 is sufficiently small

global asymptotic behavior of solutions for a parabolic parabolic ode chemotaxis system modeling multiple sclerosis abstract in this paper we focus on a chemotaxis model of multiple sclerosis which is proposed by lombardo et al 2017 10 the model consists of a chemotaxis quasi linear parabolic equation describing the evolution of the density of activated macrophages a semilinear parabolic equation ruling the evolution of the concentration of cytokine and an ordinary different equation modeling the evolution of the density of apoptotic oligodendrocytes in this model activated macrophages stimulated by a cytokine move along the concentration of cytokine gradient which is termed chemotaxis our first purpose is to rigorously prove the boundedness and global existence of the classical solution to this model by applying heat operator semigroup theory and establishing some a priori estimates the another purpose is to study the global asymptotic stability of a unique positive equilibrium which together with the turing instability are two aspects characteristic of mutual complement

new critical exponents in a fully parabolic quasilinear keller segel system and applications to volume filling models abstract we carry on our studies related to the fully parabolic quasilinear keller segel system started in 6 and continued in 7 in the above mentioned papers we proved finite time blowup of some radially symmetric solutions to the quasilinear keller segel system if the nonlinear chemosensitivity is strong enough and an adequate relation between nonlinear diffusion and chemosensitivity holds on the other hand we proved that once chemosensitivity is weak enough solutions exist globally in time the present paper is devoted to looking for critical exponents distinguishing between those two behaviors moreover we apply our results to the so called volume filling models with a power type jump probability function the most important consequence of our investigations of the latter is a critical mass phenomenon found in dimension 2 namely we find a value m such that when the solution to the two dimensional volume filling keller segel system starts with mass smaller than m then it is bounded while for some initial data with mass exceeding m solutions are unbounded though being defined for any time t 0

boundedness of solutions to a quasilinear parabolic elliptic keller segel system with logistic source abstract we study global solutions of a class of chemotaxis systems generalizing the prototype u t u 1 m 1 u u u 1 q 1 v a u b u r x t 0 0 v v u x t 0 in a bounded domain r n n 1 with smooth boundary with parameters m 1 r 1 a 0 b q 0 it is shown that when q 1 max r m 2 n or b b 0 n r m 2 r m n 2 r 2 if q 1 r then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded the results improve the results of wang et al 2014 37 and cao and zheng 2014 6

boundedness in quasilinear keller segel systems of parabolic parabolic type on non convex bounded domains abstract this paper deals with the quasilinear fully parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a bounded domain r n with smooth boundary n n the diffusivity d u is assumed to satisfy some further technical conditions such as algebraic growth and d 0 0 which says that the diffusion is allowed to be not only non degenerate but also degenerate the global in time existence and uniform in time boundedness of solutions are established under the subcritical condition that s u d u k u e for u 0 with 2 n k 0 and e 0 when d 0 0 this paper represents an improvement of tao and winkler 17 because the domain does not necessarily need to be convex in this paper in the case r n and d 0 0 uniform in time boundedness is an open problem left in a previous paper 7 this paper also gives an answer to it in bounded domains

on a parabolic elliptic system with chemotaxis and logistic type growth we consider a nonlinear pdes system of two equations of parabolic elliptic type with chemotactic terms the system models the movement of a biological population u towards a higher concentration of a chemical agent w in a bounded and regular domain rn for arbitrary n n after normalization the system is as follows ut u div um w u 1 u in t 0 t w w u in t for some positive constants m and with positive initial datum u0 and neumann boundary conditions we study the range of parameters and constrains for which the solution exists globally in time if either m 1 or m 1 and n 22 m 1 n the solution exists globally in time moreover if m 1 and 2 and there exist positive constants u 0 and u 0 such that 0 u 0 u0 u 0 we have that u 1 l w 1 l 0 as t

boundedness of solutions to a quasilinear parabolic parabolic keller segel system with a logistic source abstract we study global solutions of a class of chemotaxis systems generalizing the prototype u t u u u v a u b u r x t 0 v t v v u x t 0 in a bounded domain r n n 1 with smooth boundary u u 1 u u u 1 1 and the parameters r 1 a 0 b 0 and r it is proved that if 0 max r 1 2 n or b is big enough if r 1 then the classical solutions to the above system are uniformly in time bounded our results improve the results of wang et al 2014 28 and cao 2014 3 and also enlarge the range of the results of tao and winkler 2012 25 and ishida et al 2014 14