regularity in parabolic systems with continuous coefficients under the only assumption of continuous coefficients we prove a partial holder continuity result for solutions to parabolic systems with polynomial growth a key component throughout the argument is the use of dibenedetto s intrinsic geometry degenerate parabolic equations universitext springer new york 1993 to accommodate the inhomogeneity in the system a main technical point is that although we are proving the holder continuity of solutions we employ the intrinsic geometry using cylinder stretched according to the size of the spatial gradient in an iteration scheme that does not necessarily imply the boundedness of the gradient itself

psychometrics behind computerized adaptive testing the paper provides a survey of 18 years progress that my colleagues students both former and current and i made in a prominent research area in psychometrics computerized adaptive testing cat we start with a historical review of the establishment of a large sample foundation for cat it is worth noting that the asymptotic results were derived under the framework of martingale theory a very theoretical perspective of probability theory which may seem unrelated to educational and psychological testing in addition we address a number of issues that emerged from large scale implementation and show that how theoretical works can be helpful to solve the problems finally we propose that cat technology can be very useful to support individualized instruction on a mass scale we show that even paper and pencil based tests can be made adaptive to support classroom teaching

existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media we prove the existence of multidimensional traveling wave solutions to the scalar equation for the transport of solutes contaminants with nonlinear adsorption and spatially periodic convection diffusion adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the lax and oleinik entropy conditions in the nondegenerate case we also prove the uniqueness of the traveling waves these traveling waves are analogues of viscous shock profiles they propagate with effective speeds that depend on the periodic porous media only up to their mean states and are given by an averaged rankine hugoniot relation this is a direct consequence of the fact that the transport equation is in conservation form we use the sliding domain method the continuation method spectral theory maximum principles and a priori estimates in the degenerate case the traveling waves are weak solutions of a degenerate parabolic equation and are only holder continuous we obtain them by taking suitable limits on the non degenerate traveling waves the uniqueness of the degenerate traveling waves is open

on the cauchy problem and initial traces for a degenerate parabolic equation the authors study the cauchy problem for the degenerate parabolic equation ut div du p 2 du p 2 and find sufficient conditions on the initial trace u0 and in particular on its behaviour as x for existence of a solution in some strip rn 0 t using a harnack type inequality they show that these conditions are optimal in the case of nonnegative solutions uniqueness of solutions is shown if u0 belongs to l1loc rn but is left open in the case that u0 is merely a locally bounded measure the results are closely related to papers by aronson caffarelli benilan crandall pierre and dahlberg kenig about the porous medium equation ut um the proofs are different and allow one to generalize some of the above results to equations with variable coefficients

holder continuity of parabolic quasi minimizers abstract we are concerned with scalar valued local parabolic quasi minimizers u associated to a caratheodory integrand f obeying p growth assumptions for p 1 for such parabolic quasi minimizers we prove local holder continuity provided they are already locally bounded the superquadratic case p 2 has already been considered in 17 22 whereas the subquadratic case could at least to our knowledge not be treated in the past in this paper we are able to handle both the sub and superquadratic case under more general growth conditions

non negative solutions of the evolution p laplacian equation initial traces and cauchy problem when 1 p 2 from the introduction we continue here the investigation initiated earlier by us trans amer math soc 314 1989 no 1 187 224 concerning the solvability of the cauchy problem and the existence of initial traces for nonnegative weak solutions of the nonlinear evolution equation 1 ut div du p 2 du 0 in st rn 0 t 0 2 both in terms of results and techniques the main difference stems from the fact that unlike solutions in the case p 2 solutions of 1 are not in general locally bounded

very weak solutions of degenerate parabolic systems with non standard p x t growth abstract we study higher integrability of very weak solutions to certain degenerate parabolic systems whose model is the parabolic p x t laplacian system t u div d u p x t 2 d u div f p x t 2 f under natural assumptions on the exponent function p 0 t 2 we prove that any very weak solution u 0 t r n with d u p 1 e l 1 belongs to the natural energy space i e d u p l loc 1 provided e 0 is small enough

numerical methods and applications iterative methods based on linearization for nonlinear elliptic grid systems e g dyakonov how to solve stiff systems of differential equations by explicit methods v i lebedev on numerical methods of solving navier stokes equations in velocity pressurevariables g m kobelkov stiff systems of ordinary differential equations r p fedorenko convergence rate estimates of finite element methods for second order hyperbolic equations a a zlotnik fictitious domain methods and computation of homogenized properties of composites n s bakhvalov and a v knyazev

on latent trait estimation in multidimensional compensatory item response models making inferences from irt based test scores requires accurate and reliable methods of person parameter estimation given an already calibrated set of item parameters the latent trait could be estimated either via maximum likelihood estimation mle or using bayesian methods such as maximum a posteriori map estimation or expected a posteriori eap estimation in addition warm s psychometrika 54 427 450 1989 weighted likelihood estimation method was proposed to reduce the bias of the latent trait estimate in unidimensional models in this paper we extend the weighted mle method to multidimensional models this new method denoted as multivariate weighted mle mwle is proposed to reduce the bias of the mle even for short tests mwle is compared to alternative estimators i e mle map and eap and shown both analytically and through simulations studies to be more accurate in terms of bias than mle while maintaining a similar variance in contrast bayesian estimators i e map and eap result in biased estimates with smaller variability

remarks on holder continuity for solutions of the p laplace evolution equations we study the interior holder regularity problem for the gradient of solutions of the p laplace evolution equations with the external forces misawa gave some conditions for the holder continuity of the gradient of solutions we show holder estimates of the solutions with weaker condition as for misawa

local regularity for quasi linear parabolic equations in non divergence form abstract we consider viscosity solutions to non homogeneous degenerate and singular parabolic equations of the p laplacian type and in non divergence form we provide local holder and lipschitz estimates for the solutions in the degenerate case we prove the holder regularity of the gradient our study is based on a combination of the method of alternatives and the improvement of flatness estimates

regularity results for nonlinear parabolic obstacle problems with subquadratic growth abstract in 26 it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local holder continuous provided the obstacle is regular enough in this paper we extend this regularity result to the subquadratic case this means we establish the local holder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth more precisely we prove that d u c loc 0 2 for some 0 1 provided the coefficients and the obstacle are regular enough moreover we use the local holder continuity to prove the local lipschitz continuity of the solution u i e u c loc 0 1 1 2

well posedness and gradient blow up estimate near the boundary for a hamilton jacobi equation with degenerate diffusion abstract this paper is concerned with weak solutions of the degenerate diffusive hamilton jacobi equation t u p u u q with dirichlet boundary conditions in a bounded domain r n where p 2 and q p 1 with the goal of studying the gradient blow up phenomenon for this problem we first establish local well posedness with blow up alternative in w 1 norm we then obtain a precise gradient estimate involving the distance to the boundary it shows in particular that the gradient blow up can take place only on the boundary a regularizing effect for t u is also obtained

on the cauchy problem for the evolution p laplacian equations with gradient term and source abstract in this paper the authors study the equation u t div d u p 2 d u u q 1 u d u l in r n with p 2 we first prove that for 1 l p 1 the solution exists at least for a short time then for p 2 l p 1 the existence and nonexistence of global in time solutions are studied in various situations

item selection in multidimensional computerized adaptive testing gaining information from different angles over the past thirty years obtaining diagnostic information from examinees item responses has become an increasingly important feature of educational and psychological testing the objective can be achieved by sequentially selecting multidimensional items to fit the class of latent traits being assessed and therefore multidimensional computerized adaptive testing mcat is one reasonable approach to such task this study conducts a rigorous investigation on the relationships among four promising item selection methods d optimality kl information index continuous entropy and mutual information some theoretical connections among the methods are demonstrated to show how information about the unknown vector can be gained from different perspectives two simulation studies were carried out to compare the performance of the four methods the simulation results showed that mutual information not only improved the overall estimation accuracy but also yielded the smallest conditional mean squared error in most region of in the end the overlap rates were calculated to empirically show the similarity and difference among the four methods

local continuity and asymptotic behaviour of degenerate parabolic systems abstract we study the local holder continuity and the asymptotic behaviour of solution u u 1 u k of the degenerate system u t i m u m 1 u i for m 1 and i 1 k which describes the population densities of k species whose diffusions are determined by their total population density u u 1 u k for the local holder continuity we adopt the intrinsic scaling and iteration arguments of degiorgi moser and dibenedetto under some regularity conditions we also prove that the population density of i th species with the population m i converges in c s to the function m i m b m x t as t where b m is the barenblatt profile of the standard porous medium equation with l 1 mass m m 1 m k as a consequence of asymptotic behaviour it is shown that each density becomes a concave function after a finite time

boundedness of the gradient for a doubly nonlinear parabolic equation we prove the local boundedness of the gradient for positive solutions to a doubly nonlinear parabolic equation in the case when the standard lebesgue measure has been replaced by a doubling measure which supports a weak poincare inequality

partial regularity for subquadratic parabolic systems under controllable growth conditions in this paper we prove a regularity result for weak solutions away from singular set of parabolic systems with subquadratic growth condition of the type tu z diva z u du b z u du for z x t where the structure function a satisfies standard ellipticity and growth condition with polynomial growth rate 2nn 2 p 2 the inhomogeneity b satisfies the controllable growth condition b z u du 1 u p 1 du p 1 1p where p n 2 pn 2 p if n 2 p here p can be any exponent if n 2 p the proof is based on the a caloric approximation lemma to parabolic systems with subquadratic growth

the number of peaks of nonnegative solutions to some nonlinear degenerate parabolic equations abstract we consider the cauchy problems for some nonlinear degenerate parabolic equations in r n for nonzero bounded nonnegative initial data having compact support and show that the set of peaks of the nonnegative solution consists of one point after a finite time

self improving property of the fast diffusion equation abstract we show that the gradient of the m power of a solution to a singular parabolic equation of porous medium type also known as fast diffusion equation satisfies a reverse holder inequality in suitable intrinsic cylinders relying on an intrinsic calderon zygmund covering argument we are able to prove the local higher integrability of such a gradient for m n 2 n 2 1 our estimates are satisfied for a general class of growth assumptions on the non linearity in this way we extend the theory for m 1 see 16 in the list of references to the singular case in particular an intrinsic metric that depends on the solution itself is introduced for the singular regime

existence of weak solutions of doubly nonlinear parabolic equations abstract we deal with a cauchy dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space time cylinder for doubly nonlinear parabolic equations whose prototype is t u div u m 1 d u p 2 d u f with a non negative lebesgue function f on the right hand side where p 2 n n 2 and m 0 the central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f the constructed solution is obtained by a limit of approximations i e we use solutions of regularized cauchy dirichlet problems and pass to the limit to receive a solution for the original cauchy dirichlet problem

regularity for parabolic systems of uhlenbeck type with orlicz growth abstract we study the local regularity of p caloric functions or more generally of caloric functions in particular we study local solutions of non linear parabolic systems with homogeneous right hand side where the leading terms have uhlenbeck structure of orlicz type this paper closes the gap of 23 where liebermann proved that if the gradient of a solution is bounded it is holder continuous the crucial step is a novel local estimates for the gradient of the solutions which generalize and improve the pioneering estimates of dibenedetto and friedman 12 10 for the p laplace heat equation

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

riesz potentials and pointwise estimates of solutions to anisotropic porous medium equation abstract for an anisotropic porous medium equation with l 1 regular lower order terms we prove the local boundedness and continuity of weak solutions in terms of the linear riesz potential of the right hand side of equation

the obstacle problem for the porous medium equation we prove existence results for the obstacle problem related to the porous medium equation for sufficiently regular obstacles we find continuous solutions whose time derivative belongs to the dual of a parabolic sobolev space we also employ the notion of weak solutions and show that for more general obstacles such a weak solution exists the latter result is a consequence of a stability property of weak solutions with respect to the obstacle

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

bounded solutions to a quasilinear and singular parabolic equation with p laplacian abstract in this paper we study the existence of a positive local in time solution for the following singular nonlinear problem with homogeneous dirichlet boundary conditions t u p u u f x u u in 0 t q t u 0 on 0 t u 0 in q t u 0 x u 0 0 in where stands for a regular bounded domain of r n p u is the p laplacian defined by p u div u p 2 u 2 p 0 and t 0 the nonlinear term f r r n r is a caratheodory function satisfying the growth condition f x s a s q 1 b c p p q for a a x s r and m where a c m 0 and b 0 are some constants and q p p where p p n n p if p n and p if p n we prove for any initial nonnegative data u 0 l r with r 2 large enough the existence of at least one weak solution to p in the case 2 1 p 1 we prove the uniqueness of the solution and further regularity results for that we use some estimates based on logarithmic sobolev inequalities to get ultracontractivity of a closely related semi group of linear operators

geometric c1 α regularity estimates for nonlinear evolution models abstract in this survey we establish geometric c 1 regularity estimates for bounded solutions of a number of nonlinear evolution models in divergence and non divergence form the main insights to obtain such estimates are based on geometric tangential methods and make use of systematic oscillation mechanisms combined with intrinsic scaling techniques

life span and a new critical exponent for a doubly degenerate parabolic equation with slow decay initial values abstract in this paper we investigate the behavior of the positive solution of the following cauchy problem u t div u m p 2 u m u q with initial value decaying at infinity and give a new secondary critical exponent for the existence of global and nonglobal solutions furthermore the large time behavior and the life span of solutions are also studied

kullback leibler information and its applications in multi dimensional adaptive testing this paper first discusses the relationship between kullback leibler information kl and fisher information in the context of multi dimensional item response theory and is further interpreted for the two dimensional case from a geometric perspective this explication should allow for a better understanding of the various item selection methods in multi dimensional adaptive tests mat which are based on these two information measures the kl information index ki method is then discussed and two theorems are derived to quantify the relationship between ki and item parameters due to the fact that most of the existing item selection algorithms for mat bear severe computational complexity which substantially lowers the applicability of mat two versions of simplified kl index ski built from the analytical results are proposed to mimic the behavior of ki while reducing the overall computational intensity

higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth abstract the aim of this paper is to derive the self improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and p x t nonstandard growth more precisely we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved differential operator

the fisher kpp problem with doubly nonlinear fast diffusion abstract the famous fisher kpp reaction diffusion model combines linear diffusion with the typical fisher kpp reaction term and appears in a number of relevant applications it is remarkable as a mathematical model since in the case of linear diffusion it possesses a family of travelling waves that describe the asymptotic behaviour of a wide class of solutions 0 u x t 1 of the problem posed in the real line the existence of propagation wave with finite speed has been confirmed in the cases of slow and pseudo linear doubly nonlinear diffusion too see audrito and vazquez 2016 we investigate here the corresponding theory with fast doubly nonlinear diffusion and we find that general solutions show a non tw asymptotic behaviour and exponential propagation in space for large times finally we prove precise bounds for the level sets of general solutions even when we work in with spacial dimension n 1 in particular taking spatial logarithmic scale we show that the location of the positive level sets is approximately linear for large times this represents a strong departure from the linear case in which the location of the level sets is not purely linear but presents the celebrated logarithmic deviation for large times

cauchy problem for fast diffusion equations with a gradient term we study the cauchy problem for fast diffusion equation with a gradient term of the form ut um duq where 0 0 and 0 0 however as q m the optimality of the stipulated assumptions is left open

lorentz estimates for obstacle parabolic problems we prove that the spatial gradient of variational solutions to parabolic obstacle problems of p laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of lorentz spaces

a new online calibration method for multidimensional computerized adaptive testing multidimensional method a m method a has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing mcat chen xin paper presented at the 78th meeting of the psychometric society arnhem the netherlands 2013 however a key assumption of m method a is that it treats person parameter estimates as their true values thus this method might yield erroneous item calibration when person parameter estimates contain non ignorable measurement errors to improve the performance of m method a this paper proposes a new mcat online calibration method namely the full functional mle m method a ffmle m method a this new method combines the full functional mle jones jin in psychometrika 59 59 75 1994 stefanski carroll in annals of statistics 13 1335 1351 1985 with the original m method a in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration two correction schemes are also proposed when implementing the new method a simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original m method a in almost all conditions

the fisher kpp problem with doubly nonlinear diffusion abstract the famous fisher kpp reaction diffusion model combines linear diffusion with the typical kpp reaction term and appears in a number of relevant applications in biology and chemistry it is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 u x t 1 of the problem posed in the real line the existence of propagation waves with finite speed has been confirmed in some related models and disproved in others we investigate here the corresponding theory when the linear diffusion is replaced by the slow doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions a similar study is performed in the critical case that we call pseudo linear i e when the operator is still nonlinear but has homogeneity one with respect to the classical model and the pseudo linear case the slow travelling waves exhibit free boundaries

degenerate parabolic equations with initial data measures we address the problem of existence of solutions to degenerate and nondegenerate parabolic equations under optimal assumptions on the initial data which are assumed to be measures the requirements imposed on the initial data are connected both with the degeneracy of the principal part of the equation and with the form of the nonlinear forcing term the latter depends on the space gradient of a power of the solution applications to related problems are also outlined

cauchy problem for nonlinear parabolic equations with a gradient term we consider the cauchy problem of the nonlinear diffusive hamilton jacobi equation ut um duq where m 0 the existence and nonexistence of local and global solutions are studied by a priori estimates and compactness methods we prove that the cauchy problem of this equation has no nontrivial nonnegative global solutions if 0 moreover we obtain the global existence of solutions in the limiting case and the exact l estimates for local and global solutions

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

holder estimates for parabolic p x t laplacian systems in this paper we establish the local holder continuity of the spatial gradient of weak solutions to the parabolic p x t laplacian system begin array lll partial t u rm div left a x t du p x t 2 du right 0 end array more precisely we prove that begin array lll du in c rm loc 0 alpha alpha 2 quad rm for some alpha in 0 1 end array provided p and a are holder continuous

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

classification of blowup solutions for a parabolic p laplacian equation with nonlinear gradient terms abstract we mainly consider the following degenerate p 2 parabolic equation u t p u u m u q with homogeneous dirichlet boundary condition in a bounded domain r n before studying the properties of the solutions of this equation we first establish the local in time existence of its weak solutions then in different ranges of reaction exponents we give the complete classification of blowup results including l blowup and gradient blowup moreover under the subcritical condition of q p 1 m p 1 we can also prove that the solution is global in time

regularity of weak solutions and supersolutions to the porous medium equation abstract we investigate the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation in particular we establish the equivalence of the conditions u m l loc 2 0 t h loc 1 and u m 1 2 l loc 2 0 t h loc 1 in the definition of weak solutions our proof is based on approximation by solutions to obstacle problems

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

travelling waves in a convection diffusion equation abstract we study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1 d euclidean space the diffusion coefficient depends on the gradient in analogy with the p laplacian and may be degenerate unconditional stability is established with respect to initial data perturbations in l 1 r

multidimensional cat item selection methods for domain scores and composite scores theory and applications multidimensional computer adaptive testing mcat can provide higher precision and reliability or reduce test length when compared with unidimensional cat or with the paper and pencil test this study compared five item selection procedures in the mcat framework for both domain scores and overall scores through simulation by varying the structure of item pools the population distribution of the simulees the number of items selected and the content area the existing procedures such as volume segall in psychometrika 61 331 354 1996 kullback leibler information veldkamp van der linden in psychometrika 67 575 588 2002 minimize the error variance of the linear combination van der linden in j educ behav stat 24 398 412 1999 and minimum angle reckase in multidimensional item response theory springer new york 2009 are compared to a new procedure minimize the error variance of the composite score with the optimized weight proposed for the first time in this study the intent is to find an item selection procedure that yields higher precisions for both the domain and composite abilities and a higher percentage of selected items from the item pool the comparison is performed by examining the absolute bias correlation test reliability time used and item usage three sets of item pools are used with the item parameters estimated from real live cat data results show that volume and minimum angle performed similarly balancing information for all content areas while the other three procedures performed similarly with a high precision for both domain and overall scores when selecting items with the required number of items for each domain the new item selection procedure has the highest percentage of item usage moreover for the overall score it produces similar or even better results compared to those from the method that selects items favoring the general dimension using the general model segall in psychometrika 66 79 97 2001 the general dimension method has low precision for the domain scores in addition to the simulation study the mathematical theories for certain procedures are derived the theories are confirmed by the simulation applications

holder zygmund estimates for degenerate parabolic systems abstract we consider energy solutions of the inhomogeneous parabolic p laplacian system t u div d u p 2 d u div g we show in the case p 2 that if the right hand side g is locally in l bmo then u is locally in l c 1 where c 1 is the 1 holder zygmund space this is the borderline case of the calderon zygmund theory we provide local quantitative estimates we also show that finer properties of g are conserved by du e g holder continuity moreover we prove a new decay for gradients of p caloric solutions for all 2 n n 2 p

harnack estimates for quasi linear degenerate parabolic differential equations we establish the intrinsic harnack inequality for non negative solutions of a class of degenerate quasilinear parabolic equations including equations of the p laplacian and porous medium type it is shown that the classical harnack estimate while failing for degenerate parabolic equations it continues to hold in a space time geometry intrinsic to the degeneracy the proof uses only measure theoretical arguments it reproduces the classical moser theory for non degenerate equations and it is novel even in that context holder estimates are derived as a consequence of the harnack inequality the results solve a long standing problem in the theory of degenerate parabolic equations

regularity of solutions of nonlinear degenerate parabolic systems soit le systeme parabolique u i t div u p 2 u i 0 i m avec p 1 ou u i u i x t grad x et x r n ouvert pour toute solution de ce systeme avec max 1 2n n 2 p u est continu dans t

weak solutions of the porous medium equation we show that if u 0 u l loc m r n 1 solves u t u m m 1 in the sense of distributions then u is locally holder continuous in

the asymptotic behaviour of solutions of a porous medium equation with bounded measurable coefficients abstract we prove the holder continuity of the interface of a solution of a porous medium equation with bounded measurable coefficients we also describe the asymptotic behaviour as time goes to infinity

global gradient estimates for non quadratic vector valued parabolic quasi minimizers abstract we establish local and global higher integrability estimates for the gradient of vector valued parabolic quasi minimizers of integral functionals with polynomial p growth p 2 n n 2 on a parabolic domain t in r n 1 n 2 and under a weak regularity assumption on the parabolic boundary of t

on the fuzzy difference equations of finance in this paper our intention is to demonstrate the applicability of fuzzy difference equations in the field of finance in order to achieve that we follow the work done by deeba et al and papashinopoulos et al and we study the existence of positive solutions to fuzzy financial difference equations initially we appose a method realized by buckley that deals with fuzzy analogues of the elementary compound interest problem afterwards we approach this case via the fuzzy difference equations method after making a comparison between the two methods we notice that they end up to the same general formula the main contribution of this paper is the simplicity of the method presented which gives us the opportunity to create formulas for cases which are specialized and also more realistic than the very basic one of the compound interest moreover by using difference equations we can study the factors which cause the change in the value of money in different time periods as a source for these cases of finance we use the work of kwapisz and we study a well known problem of financial mathematics this problem deals with the time value of money and as a direct application of it we study the balance of bank deposits finally a numerical example is presented for better understanding

travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains abstract for a fixed bounded domain d r n we investigate the asymptotic behaviour for large times of solutions to the p laplacian diffusion equation posed in a tubular domain t u p u in d r t 0 with p 2 i e the slow diffusion case and homogeneous dirichlet boundary conditions on the tube boundary passing to suitable re scaled variables we show the existence of a travelling wave solution in logarithmic time that connects the level u 0 and the unique nonnegative steady state associated to the re scaled problem posed in a lower dimension i e in d r n we then employ this special wave to show that a wide class of solutions converge to the universal stationary profile in the middle of the tube and at the same time they spread in both axial tube directions miming the behaviour of the travelling wave and its reflection for large times the first main feature of our analysis is that wave fronts are constructed through a nonstandard combination of diffusion and absorbing boundary conditions which gives rise to a sort of fisher kpp long time behaviour the second one is that the nonlinear diffusion term plays a crucial role in our analysis actually in the linear diffusion framework p 2 solutions behave quite differently

a transport model with micro and macro structure abstract in this paper we consider solute transport through porous media where the chemical species undergoes a chemical process through the surface of the porous skeleton the problem is modeled by a system of differential equations for the macro concentration u u x t and the micro concentration u u x x t we prove existence and uniqueness and some properties of the set with positive concentration

continuity estimates for porous medium type equations with measure data abstract we consider parabolic equations of porous medium type of the form u t div a x t u d u in e t in some space time cylinder e t the most prominent example covered by our assumptions is the classical porous medium equation u t u m in e t with m 1 we establish a sufficient condition for the continuity of u in terms of a natural riesz potential of the right hand side measure as an application we come up with a borderline condition ensuring the continuity of u more precisely if l n 2 2 1 then u is continuous in e t

multidimensional adaptive testing with optimal design criteria for item selection several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing in particular it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional some should be considered as a nuisance or the interest is in the testing of a composite of the abilities both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of a optimality and d optimality lead to the most accurate estimates when all abilities are intentional with the former slightly outperforming the latter the criterion of e optimality showed occasional erratic behavior for this case of adaptive testing and its use is not recommended if some of the abilities are nuisances application of the criterion of as optimality or ds optimality which focuses on the subset of intentional abilities is recommended for the measurement of a linear combination of abilities the criterion of c optimality yielded the best results the preferences of each of these criteria for items with specific patterns of parameter values was also assessed it was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters