the affine polya szego principle equality cases and stability a brothers ziemer type theorem for the affine polya szego principle and a quantitative affine polya szego principle are established

affine orlicz polya szego principle for log concave functions abstract the affine l p polya szego principle significantly strengthens the classical polya szego principle it is an open problem whether there exists an affine orlicz polya szego principle which includes the affine l p polya szego principle as special case in this paper an affine orlicz polya szego principle for log concave functions is established by using functional steiner symmetrizations

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

parametrically controlling solitary wave dynamics in the modified korteweg de vries equation we demonstrate the control of solitary wave dynamics of the modified korteweg de vries mkdv equation through the temporal variations of the distributed coefficients this is explicated through exact cnoidal wave and localized soliton solutions of the mkdv equation with variable coefficients the solitons can be accelerated and their propagation can be manipulated by suitable variations of the above parameters in sharp contrast with the nonlinear schrodinger equation the soliton amplitude and widths are time independent

approximate similarity reduction for the perturbed mkdv equation via symmetry perturbation and direct method the perturbed mkdv equation with the general form is investigated in terms of the approximate symmetry perturbation method and the approximate direct method the similarity reduction solutions of different orders are obtained for both methods series reduction solutions are consequently derived higher order similarity reduction equations are linear variable coefficient ordinary differential equations by comparison the relation between the results obtained by applying the two methods is revealed

new polya szego type inequalities and an alternative approach to comparison results for pde s abstract we prove some polya szego type inequalities which involve couples of functions and their rearrangements our inequalities reduce to the classical polya szego principle when the two functions coincide as an application we give a different proof of a comparison result for solutions to dirichlet boundary value problems for laplacian equations proved in 1

hardy spaces and the two dimensional euler equations with nonnegative vorticity we prove that certain quadratic expressions involving the gradient of a weakly superharmonic function in r belong to a local hardy space as an application we provide a new proof of j m delort s convergence theorem for solutions of the two dimensional euler equations with vorticities of one sign department of mathematics university of california berkeley california 94720 sfb 256 institut fur angewandte mathematik beringstrasse 4 d5300 bonn 1 ger many this content downloaded from 207 46 13 101 on sat 08 oct 2016 05 44 35 utc all use subject to http about jstor org terms

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

symmetrization with respect to the anisotropic perimeter and applications in this paper we introduce a new type of symmetrization which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function in order to prove sharp comparison results for solutions of a class of homogeneous dirichlet fully nonlinear elliptic problems of second order and for suitable anisotropic hessian integrals

burgers equation for kinetic clustering in traffic flow abstract a kinetic clustering of cars is analyzed using a limiting procedure and a reductive perturbation method by using the limiting procedure the difference difference equation to describe the clustering is obtained we derive the coarse grained equation describing the hydrodynamic mode using the reductive perturbation method it is shown that this hydrodynamic equation is given by the burgers equation and that the typical headway and velocity scale as t1 2 and t 1 2 in time for the initial random velocity distribution

theoretical analysis of the density wave in a new continuum model and numerical simulation abstract considered the effect of traffic anticipation in the real world a new anticipation driving car following model ad cf was proposed by zheng et al based on ad cf model adopted an asymptotic approximation between the headway and density a new continuum model is presented in this paper the neutral stability condition is obtained by applying the linear stability theory additionally the korteweg de vries kdv equation is derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the neutral stability line the numerical simulation and the analytical results show that the new continuum model is capable of explaining some particular traffic phenomena

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

reduced hausdorff dimension and concentration cancellation for two dimensional incompressible flow where v t v1 v2 is the fluid velocity p is the scalar pressure dv dt av at v v v and vo is an initial incompressible velocity field i e div vo 0 in this paper we study the detailed limiting behavior of approximate solution sequences for 2 d euler with vortex sheet initial data a sequence of smooth velocity fields v8 x t is an approximate solution sequence for 2 d euler provided that v is incompressible i e div v 0 and satisfies the following properties 1 the velocity fields v6 have uniformly bounded local kinetic energy i e

renormalization and energy conservation for axisymmetric fluid flows we study vanishing viscosity solutions to the axisymmetric euler equations without swirl with relative vorticity in l p with p 1 we show that these solutions satisfy the corresponding vorticity equations in the sense of renormalized solutions moreover we show that the kinetic energy is preserved provided that p 3 2 and the vorticity is nonnegative and has finite second moments

nonlinear analysis in the aw rascle anticipation model of traffic flow in this paper the aw rascle anticipation ara model is discussed from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic for this purpose a nonlinear traffic flow stability criterion is derived by using a wavefront expansion technique the result of the nonlinear stability analysis can be used not only to judge the stability evolution of an initial traffic state but also to determine the pressure term in the ara model the kdv equation is derived from the ara model added by the viscous term with the use of the reduction perturbation method the soliton solution can be analytically obtained from the perturbed kdv equation only near the neutral stability line weighted essentially nonoscillatory schemes are employed to simulate the kdv soliton the numerical results confirm the analytical kdv soliton solution

lagrangian solutions to the vlasov poisson system with l1 density the recently developed theory of lagrangian flows for transport equations with low regularity coefficients enables to consider non bv vector fields we apply this theory to prove existence and stability of global lagrangian solutions to the repulsive vlasov poisson system with only integrable initial distribution function with finite energy these solutions have a well defined lagrangian flow an a priori estimate on the smallness of the superlevels of the flow in three dimensions is established in order to control the characteristics

jamming transition in traffic flow on triangular lattice abstract phase transitions and critical phenomena are investigated in the two dimensional traffic flow on the triangular lattice numerically and analytically the two dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a site it is shown that the jamming transition between the freely moving and jammed phases depends on the configuration of car moving directions it is found that the three distinct jamming transitions occur the conventional jamming transition to the kink jams the jamming transition to the chaotic jams and the jamming transition to the oscillating jams the conventional jamming transition to the kink jams is analyzed by the use of the linear stability theory and the nonlinear method the coexisting curve between the freely moving and jammed phases is calculated from the solution of the modified korteweg de vries kdv equation

nonlinear analysis of traffic flow on a gradient highway abstract we investigate the slope effects upon traffic flow on a single lane gradient uphill downhill highway analytically and numerically the stability condition neutral stability condition and instability condition are obtained by the use of linear stability theory it is found that stability of traffic flow on the gradient varies with the slopes the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived to describe the triangular shock waves soliton waves and kink antikink waves in the stable meta stable and unstable region respectively a series of simulations are carried out to reproduce the triangular shock waves kink antikink waves and soliton waves results show that amplitudes of the triangular shock waves and kink antikink waves vary with the slopes the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance moreover both the kink antikink waves and the solitary waves propagate backwards the numerical simulation shows a good agreement with the analytical result

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

convex symmetrization and polya szego inequality abstract we prove a polya szego inequality involving a convex symmetrization of functions and we investigate the equality case

a uniqueness proof for the wulff theorem the wulff problem is a generalisation of the isoperimetric problem and is relevant for the equilibrium of small elastic crystals it consists in minimising the generally anisotropic surface energy among sets of given volume a solution of this problem is given by a geometric construction due to wulff in the class of sets of finite perimeter this was first shown by j e taylor who using methods of geometric measure theory also proved uniqueness here a more analytic uniqueness proof is presented the main ingredient is a sharpened version of the brunn minkowski inequality

continuity equations and ode flows with non smooth velocity in this paper we review many aspects of the well posedness theory for the cauchy problem for the continuity and transport equations and for the ordinary differential equation ode in this framework we deal with velocity fields that are not smooth but enjoy suitable weak differentiability assumptions we first explore the connection between the partial differential equation pde and the ode in a very general non smooth setting then we address the renormalization property for the pde and prove that such a property holds for sobolev velocity fields and for bounded variation velocity fields finally we present an approach to the ode theory based on quantitative estimates

density waves in the continuum analog of the full velocity difference model abstract a continuum version of the car following full velocity difference model fvdm is developed using a series expansion of the headway in terms of the density this continuum model obeys the equivalent stability criterion as its discrete counterpart and the burgers and korteweg de vries equations deriving from the analogous continuum model are equivalent to their counterparts from the transformed car following model

interpolation between brezis vazquez and poincare inequalities on nonnegatively curved spaces sharpness and rigidities abstract this paper is devoted to investigate an interpolation inequality between the brezis vazquez and poincare inequalities shortly bpv inequality on nonnegatively curved spaces as a model case we first prove that the bpv inequality holds on any minkowski space by fully characterizing the existence and shape of its extremals we then prove that if a complete finsler manifold with nonnegative ricci curvature supports the bpv inequality then its flag curvature is identically zero in particular we deduce that a berwald space of nonnegative ricci curvature supports the bpv inequality if and only if it is isometric to a minkowski space our arguments explore fine properties of bessel functions comparison principles and anisotropic symmetrization on minkowski spaces as an application we characterize the existence of nonzero solutions for a quasilinear pde involving the finsler laplace operator and a hardy type singularity on minkowski spaces where the sharp bpv inequality plays a crucial role the results are also new in the riemannian euclidean setting

functions of bounded variation and rearrangements the action of the symmetric rearrangement of functions of bounded variation is investigated in particular pointwise regularizing effects are established polya szeg type inequalities with a characterization of equality cases are also proved

a quantitative polya szego principle andrea cianchidipartimento di matematica e applicazioni per l architetturapiazza ghiberti 27 50122 firenze italye mail cianchi uni itluca espositodipartimento di ingegneria dell informazione e matematica applicatavia ponte don melillo 84084 fisciano sa italye mail esposito diima unisa itnicola fuscodipartimento di matematica e applicazionivia cintia 80126 napoli italye mail n fusco unina itcristina trombettidipartimento di matematica e applicazionivia cintia 80126 napoli italye mail cristina unina itjune 27 2006

lagrangian solutions to the 2d euler system with l1 vorticity and infinite energy we consider solutions to the two dimensional incompressible euler system with only integrable vorticity thus with possibly locally infinite energy with such regularity we use the recently developed theory of lagrangian flows associated to vector fields with gradient given by a singular integral in order to define lagrangian solutions for which the vorticity is transported by the flow we prove strong stability of these solutions via strong convergence of the flow under the only assumption of l1 weak convergence of the initial vorticity the existence of lagrangian solutions to the euler system follows for arbitrary l1 vorticity relations with previously known notions of solutions are established

estimates and regularity results for the diperna lions flow in this paper we derive new simple estimates for ordinary differential equations with sobolev coefficients these estimates not only allow to recover some old and recent results in a simple direct way but they also have some new interesting corollaries