the asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors abstract in this paper we study the asymptotic behavior of globally smooth solutions of the cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in r d we prove that smooth solutions close to equilibrium of the problem converge to a stationary solution exponentially fast as t

relaxation limit and initial layer to hydrodynamic models for semiconductors abstract we study a relaxation limit of a solution to the initial boundary value problem for a hydrodynamic model to a drift diffusion model over a one dimensional bounded domain it is shown that the solution for the hydrodynamic model converges to that for the drift diffusion model globally in time as a physical parameter called a relaxation time tends to zero it is also shown that the solutions to the both models converge to the corresponding stationary solutions as time tends to infinity respectively here the initial data of electron density for the hydrodynamic model can be taken arbitrarily large in the suitable sobolev space provided that the relaxation time is sufficiently small because the drift diffusion model is a coupled system of a uniformly parabolic equation and the poisson equation since the initial data for the hydrodynamic model is not necessarily in momentum equilibrium an initial layer should occur however it is shown that the layer decays exponentially fast as a time variable tends to infinity and or the relaxation time tends to zero these results are proven by the decay estimates of solutions which are derived through energy methods

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

loewner matrices and operator convexity let f be a function from mathbb r into itself a classic theorem of k lowner says that f is operator monotone if and only if all matrices of the form left frac f p i f p j p i p j right vphantom x x 1 are positive semidefinite we show that f is operator convex if and only if all such matrices are conditionally negative definite and that f t t g t for some operator convex function g if and only if these matrices are conditionally positive definite elementary proofs are given for the most interesting special cases f t t r and f t t log t several consequences are derived

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

contractive maps on operator ideals and norm inequalities ii abstract let i be a norm ideal of operators equipped with a unitarily invariant norm we exploit integral representations of certain functions to prove that certain ratios of linear operators acting on operators in i are contractive this leads to some new and old norm inequalities we also lift a variety of inequalities to the operator setting which were proved in the matrix setting earlier

existence and some limits of stationary solutions to a one dimensional bipolar euler poisson system abstract in this paper we study the stationary flow for a one dimensional isentropic bipolar euler poisson system hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron and hole densities and their current densities coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we first show the unique existence of stationary solutions of the one dimensional isentropic hydrodynamic model based on the schauder fixed point principle and the careful energy estimates next we investigate the zero electron mass limit combined zero electron mass and zero hole mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we also show the strong convergence of the sequence of solutions and give the associated convergence rates

asymptotic behavior of solutions to euler poisson equations for bipolar hydrodynamic model of semiconductors abstract in this paper we study the cauchy problem for 1 d euler poisson system which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non flat doping profile different from the previous studies gasser et al 2003 7 huang et al 2011 12 huang et al 2012 13 for the case with two identical pressure functions and zero doping profile we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves steady state solutions rather than the diffusion waves furthermore we prove that when the flow is fully subsonic by means of a technical energy method with some new development the smooth solutions of the system are unique exist globally and time algebraically converge to the corresponding stationary solutions the optimal algebraic convergence rates are obtained

operator monotone functions jacobi operators and orthogonal polynomials abstract we reveal a connection between operator monotone functions and orthogonal polynomials especially we express an operator monotone function with a jacobi operator and show that it is a limit of rational operator monotone functions further we prove that the principal inverse of an orthogonal polynomial is operator monotone and hence it has a holomorphic extension to the open upper half plane namely a pick function or nevanlinna function

subsonic flow for the multidimensional euler poisson system we establish the existence and stability of subsonic potential flow for the steady euler poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on a non insulated boundary from a fixed point at the exit and prescribing the pressure at the exit of the nozzle the euler poisson system for subsonic potential flow can be reduced to a nonlinear elliptic system of second order in this paper we develop a technique to achieve a priori c 1 alpha estimates of solutions to a quasi linear second order elliptic system with mixed boundary conditions in a multidimensional domain enclosed by a lipschitz continuous boundary in particular we discovered a special structure of the euler poisson system which enables us to obtain c 1 alpha estimates of the velocity potential and the electric potential functions and this leads us to establish structural stability of subsonic flows for the euler poisson system under perturbations of various data

higher regularity of the tangential fields in the relativistic vlasov maxwell system abstract it is shown that the tangential electric and magnetic fields in the glassey strauss representation formulas are in fact bounded in l loc t l x 2 for some 0

diffusion relaxation limit of a bipolar hydrodynamic model for semiconductors in the paper we discuss the relaxation limit of a bipolar isentropic hydrodynamical models for semiconductors with small momentum relaxation time with the help of the maxwell iteration we prove that as the relaxation time tends to zero periodic initial value problems of a scaled bipolar isentropic hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift diffusion model has smooth solutions meanwhile we justify a formal derivation of the corresponding drift diffusion model from the bipolar hydrodynamic model

norm inequalities in operator ideals abstract in this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm among the well known inequalities which can be proved with this technique are the lowner heinz inequality inequalities relating various operator means and the corach porta recht inequality we prove two general inequalities and from them we derive several inequalities by specialization many of them new we also show how some inequalities known to be valid for matrices or bounded operators can be extended with this technique to normed ideals in c algebras in particular to the noncommutative l p spaces of a semi finite von neumann algebra

classical solutions and the glassey strauss theorem for the 3d vlasov maxwell system r glassey and w strauss have proved in arch rational mech anal 92 1986 59 90 that c1 solutions to the relativistic vlasov maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded the present paper simplifies their proof

interpolating the arithmetic geometric mean inequality and its operator version two families of means called heinz means and heron means that interpolate between the geometric and the arithmetic mean are considered comparison inequalities between them are established operator versions of these inequalities are obtained failure of such extensions in some cases is illustrated by a simple example

arithmetic geometric mean and related inequalities for operators abstract in recent years certain arithmetic geometric mean and related inequalities for operators and unitarily invariant norms have been obtained by many authors based on majorization technique and so on we first point out that they are direct consequences of integral expressions of relevant operators furthermore we obtain related new inequalities theorems 4 5 and 6 based on our current approach

global existence for the system of the macroscopic balance equations of charge transport in semiconductors abstract global existence of a solution to the nonlinear balance equations of charge transport in semiconductors based on the maximum entropy principle contin mech thermodyn 11 1999 307 325 contin mech thermodyn 12 2000 31 51 is proven for a typical 1d problem under certain restrictions on the doping profile and the initial data

positivity properties of some special matrices abstract it is shown that for positive real numbers 0 1 n 1 i j where denotes the beta function is infinitely divisible and totally positive for 1 i j the cholesky decomposition and successive elementary bidiagonal decomposition are computed let w n be the nth bell number it is proved that w i j is a totally positive matrix but is infinitely divisible only upto order 4 it is also shown that the symmetrized stirling matrices are totally positive

families of completely positive maps associated with monotone metrics abstract an operator convex function on 0 which satisfies the symmetry condition k x 1 x k x can be used to define a type of non commutative multiplication by a positive definite matrix or its inverse using the primitive concepts of left and right multiplication and the functional calculus the operators for the inverse can be used to define quadratic forms associated with riemannian metrics which contract under the action of completely positive trace preserving maps we study the question of when these operators define maps which are also completely positive cp although a d 1 2 a d 1 2 is the only case for which both the map and its inverse are cp there are several well known one parameter families for which either the map or its inverse is cp we present a complete analysis of the behavior of these families as well as the behavior of lines connecting an extreme point with the smallest one and some results for geometric bridges between these points our primary tool is an order relation based on the concept of positive definite functions although some results can be obtained from known properties we also prove new results based on the positivity of the fourier transforms of certain functions concrete computations of certain fourier transforms not only yield new examples of positive definite functions but also examples in the much stronger class of infinitely divisible functions

the zero electron mass limit for a stationary nonisentropic hydrodynamic semiconductor model in this paper we study a general multidimensional nonisentropic hydrodynamical model for semiconductors the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation for steady state subsonic and potential flows we discuss the zero electron mass limit of system by using the method of asymptotic expansions we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order

a new continuation criterion for the relativistic vlasov maxwell system the global existence of solutions to the relativistic vlasov maxwell system given sufficiently regular finite energy initial data is a longstanding open problem the main result of glassey and strauss arch ration mech anal 92 59 90 1986 shows that a solution f e b remains c 1 as long as the momentum support of f remains bounded alternate proofs were later given by bouchut et al arch ration mech anal 170 1 15 2003 and klainerman and staffilani commun pure appl anal 1 103 125 2002 we show that only the boundedness of the momentum support of f after projecting to any two dimensional plane is needed for f e b to remain c 1

singularities of solutions to the compressible euler equations and euler poisson equations with damping in this paper we consider the formation of singularities of solutions to the compressible euler equations with damping and pressureless euler poisson equations with damping under certain assumptions of the initial data we can get the blow up result of the solutions in the finite time in this paper we consider the formation of singularities of solutions to the compressible euler equations with damping and pressureless euler poisson equations with damping under certain assumptions of the initial data we can get the blow up result of the solutions in the finite time

global smooth solutions to the multidimensional hydrodynamic model for plasmas with insulating boundary conditions the existence of global smooth solutions to the multidimensional hydrodynamic model for plasmas of electrons and positively charged ions with insulating boundary conditions is shown under the assumption that the initial densities are close to a constant furthermore it is proved that the particle densities converge exponentially fast to the constant steady state

riemannian metrics on positive definite matrices related to means abstract the riemannian metric on the manifold of positive definite matrices is defined by a kernel function in the form k d h k i j i j 1 tr p i hp j k when i i p i is the spectral decomposition of the foot point d and the hermitian matrices h k are tangent vectors for such kernel metrics the tangent space has an orthogonal decomposition the pull back of a kernel metric under a mapping d g d is a kernel metric as well several riemannian geometries of the literature are particular cases for example the statistical metric for multivariate gaussian distributions and the quantum fisher information in the paper the case x y m x y is mostly studied when m x y is a mean of the positive numbers x and y there are results about the geodesic curves and geodesic distances the geometric mean the logarithmic mean and the root mean are important cases

stability of periodic steady state solutions to a non isentropic euler poisson system abstract we study the stability of periodic smooth solutions near non constant steady states for a non isentropic euler poisson system without temperature damping term the system arises in the theory of semiconductors for which the doping profile is a given smooth function in this stability problem there are no special restrictions on the size of the doping profile but only on the size of the perturbation we prove that small perturbations of periodic steady states are exponentially stable for large time for this purpose we introduce new variables and choose a non diagonal symmetrizer of the full euler equations to recover dissipation estimates this also allows to make the proof of the stability result very simple and concise

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

matrix power means and the karcher mean we define a new family of matrix means pt a t 1 1 where and a vary over all positive probability vectors in rn and n tuples of positive definite matrices resp each of these means except t 0 arises as a unique positive definite solution of a non linear matrix equation satisfies all desirable properties of power means of positive real numbers and interpolates between the weighted harmonic and arithmetic means the main result is that the karcher mean coincides with the limit of power means as t 0 this provides not only a sequence of matrix means converging to the karcher mean but also a simple proof of the monotonicity of the karcher mean conjectured by bhatia and holbrook and other new properties which have recently been established by lawson and lim and also bhatia and karandikar using probabilistic methods on the metric structure of positive definite matrices equipped with the trace metric

on infinite divisibility of positive definite functions arising from operator means abstract for a point wisely non negative positive definite function a certain criterion for its infinite divisibility i e all its fractional powers are also positive definite is obtained this criterion enables us to show infinite divisibility for many positive definite functions appearing naturally in study of operator means in particular we determine when the function cosh x s cosh x s 0 1 s s 1 1 is infinitely divisible

critical thresholds in 2d restricted euler poisson equations we provide a complete description of the critical threshold phenomenon for the two dimensional localized euler poisson equations introduced by the authors in comm math phys 228 2002 pp 435 466 here the questions of global regularity vs finite time breakdown for the two dimensional 2d restricted euler poisson solutions are classified in terms of precise explicit formulae describing a remarkable variety of critical threshold surfaces of initial configurations in particular it is shown that the 2d critical thresholds depend on the relative sizes of three quantities the initial density the initial divergence and the initial spectral gap that is the difference between the two eigenvalues of the 2 2 initial velocity gradient

stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species abstract we discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species we consider not only the mass and momentum equations for electrons but also those two equations for holes the recombination effects between electrons and holes are taken into consideration as well we study the case where the doping profile is close to zero and depends on the spacial variable x we shall show that steady state solutions are asymptotically stable

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

some results on matrix monotone functions abstract let a and b be hermitian matrices we say that a b if a b is nonnegative definite a function 0 r is said to be matrix monotone m m if a b 0 implies that a b matrix convex and concave functions can be similarly defined in this paper several known results some in sharper forms are given alternative proofs these include the following a a positive function t is m m iff t t is m m b if t is m m then both t t and t t are matrix convex and are almost always strictly convex on the other hand t is always concave and almost always strictly concave the concavity of m m functions and an inequality of hansen are consequences of a more general inequality on m m functions some complementary inequalities are also established we then prove an extension of lyapunov s theorem let a and p be positive definite matrices and either or 1 be a m m function then the unique matrix solution x of the matrix equation ax xa a p p a is positive definite a similar result holds for a related equation most of the results are obtained by exploiting the integral representation of m m functions

thresholds in three dimensional restricted euler poisson equations abstract this work provides a description of the critical threshold phenomenon in multi dimensional restricted euler poisson rep equations introduced in h liu e tadmor spectral dynamics of the velocity gradient field in restricted fluid flows comm math phys 228 2002 435 466 for three dimensional rep equations we identified both upper thresholds for the finite time blow up of solutions and subthresholds for the global existence of solutions with the thresholds depending on the relative size of the eigenvalues of the initial velocity gradient matrix and the initial density for the attractive forcing case these one sided threshold conditions of the initial configurations are optimal and the corresponding results also hold for arbitrary n dimensions n 3

asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors abstract we study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included we study the case where the flow is subsonic and the doping profile is close to a negative constant depending on the spacial variablex we shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfiesp 0 wherepis defined in 3 5

regularity symmetry and uniqueness of some integral type quasilinear equations abstract we study integral equations corresponding to some quasilinear equations with nonlinearities of lane emden and hartree type regularity symmetry and uniqueness of these equations are considered we obtain the uniqueness of the ground state of h 1 critical hartree equation and extend the moving plane method of integral equation in w chen c li b ou classification of solutions for an integral equation comm pure appl math lix 2006 0330 0343 w chen c li b ou classification of solutions for a system of integral equations comm partial differential equations 30 1 3 2005 59 65 to some integral equations corresponding to the p laplace equation we use ideas from the potential theories for the p laplace equations and hessian equations

nonlinear asymptotic stability of the equilibrium state for the mep model of charge transport in semiconductors abstract nonlinear asymptotic lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle a m anile v romano non parabolic band transport in semiconductors closure of the moment equations contin mech thermodyn 11 1999 307 325 v romano non parabolic band transport in semiconductors closure of the production terms in the moment equations contin mech thermodyn 12 2000 31 51 is proven for a typical 1 d problem

operator inequalities from a general theorem to concrete inequalities abstract the aim of this paper is to give a method to extract concrete inequalities from a general theorem which is established by making use of majorization relation between functions by this method we can get a lot of inequalities among others we extend furuta inequality as follows let f i g j be positive operator monotone functions on 0 and put k t t r 0 f 1 t r 1 f m t r m h t t p 0 g 1 t p 1 g n t p n where p 0 1 and r i 0 p j 0 then 0 a c b implies for 0 1 r 0 p r 0 with p p 0 p n k c 1 2 h a k c 1 2 k c 1 2 h c k c 1 2 k c 1 2 h b k c 1 2 moreover we show log c 1 2 e a c 1 2 log c 1 2 e c c 1 2 log c 1 2 e b c 1 2 provided c is invertible we also refer to operator geometric mean

the singular values of a b and a ib we obtain several inequalities relating the singular values of a b and those of a ib when a and b are hermitian and when one or both of them are positive semidefinite

large time behavior of the solutions to a hydrodynamic model for semiconductors we establish the global existence of smooth solutions to the cauchy problem for the one dimensional isentropic euler poisson or hydrodynamic model for semiconductors for small initial data in particular we show that as t to infty these solutions converge to the stationary solutions of the drift diffusion equations the existence and uniqueness of stationary solutions to the drift diffusion equations are proved without the smallness assumption

weak solutions to isothermal hydrodynamic model for semiconductor devices abstract in this paper the cauchy problem of the isothermal hydrodynamic model for semiconductor devices is investigated the existence of global weak entropy solutions with large initial data is obtained by using a modified fractional step lax friedrichs scheme and the theory of compensated compactness as a byproduct the existence of entropy solutions to the cauchy problem of the isentropic hydrodynamic model for a semiconductor with infinite mass is also proved

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

on the regularity of positive solutions of a class of choquard type equations this paper is concerned with positive solutions of a class of choquard type equations such equations are equivalent to integral systems involving the bessel potential and the riesz potential by using two regularity lifting lemmas introduced by chen and li 2 we study the regularity for integrable solutions u we first use the hardy littlewood sobolev inequality to obtain an integrability result then it is improved to u in l s r n for all s in 1 infty by an iteration next we use the properties of the contraction map and the shrinking map to prove that u is lipschitz continuous finally we establish the smoothness of u by a bootstrap argument our technique can also be used to handle other integral systems involving the riesz potential or the bessel potential such as the hartree type equations

relaxation time limit of the multidimensional bipolar hydrodynamic model in besov space abstract in this paper we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas this system takes the form of the bipolar euler poisson model with electric field and frictional damping added to the momentum equations in the framework of the besov space theory we establish the global existence of smooth solutions for cauchy problems when the initial data are sufficiently close to the constant equilibrium next based on the special structure of the nonlinear system we also show the uniform estimate of solutions with respect to the relaxation time by the high and low frequency decomposition methods finally we discuss the relaxation time limit by compact arguments that is it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift diffusion model as the relaxation time tends to zero

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

strong monotonicity for various means abstract point wise monotonicity in parameters for various one parameter families of scalar means such as power difference means binomial means and stolarsky means is well known but norm comparison for corresponding operator means requires monotonicity in the sense of positive definiteness among other things we obtain monotonicity in the sense of infinite divisibility which is much stronger than that in the sense of positive definiteness these strong monotonicity results are proved based on explicit computations for measures in relevant levy khintchine or actually kolmogorov formulas

relaxation limit in bipolar semiconductor hydrodynamic model with non constant doping profile abstract the relaxation limit from bipolar semiconductor hydrodynamic hd model to drift diffusion dd model is shown under the non constant doping profile assumption for both stationary solutions and global in time solutions which satisfy the general form of the ohmic contact boundary condition the initial layer phenomenon will be analyzed because the initial data is not necessarily in the momentum equilibrium due to the bipolar coupling structure the analysis is hard and different from the previous literature on unipolar model or bipolar model with zero doping profile restriction we first construct the non constant uniform stationary solutions by the operator method for both hd and dd models in a unified procedure then we prove the global existence of dd model and uniform global existence of hd model by the elementary energy method but with some new developments based on the above existence results we further calculate the convergence rates in relaxation limits

geometric mean block matrices abstract we consider an m m block matrix g with entries a i a j where a 1 a m are positive definite matrices of fixed size and a b is the geometric mean of positive definite matrix a and b we show that g is positive semidefinite if and only if the family of a 1 a m is commuting it can be transformed to a commuting family of positive definite matrices by a congruence transformation this result via commuting families provides not only a kind of positive semidefinite block matrices but also a new extremal characterization of two variable geometric mean in terms of multivariate block matrices

mean matrices and infinite divisibility abstract we consider matrices m with entries mij m i j where 1 n are positive numbers and m is a binary mean dominated by the geometric mean and matrices w with entries wij 1 m i j where m is a binary mean that dominates the geometric mean we show that these matrices are infinitely divisible for several much studied classes of means

the asymptotic behavior of global smooth solutions to the hydrodynamic model for semiconductors with spherical symmetry abstract in this paper we study the asymptotic behavior of the global smooth solutions to the initial boundary value problem for the hydrodynamic model for semiconductors with spherical symmetry we prove that the solution to the problem converges to a stationary solution time asymptotically exponentially fast

global solutions to compressible navier stokes poisson and euler poisson equations of plasma on exterior domains abstract the initial boundary value problems for compressible navier stokes poisson and euler poisson equations of plasma are considered on exterior domains in this paper with the radial symmetry assumption the global existence of solutions to compressible navier stokes poisson equations with the large initial data on a domain exterior to a ball in r n n 1 is proved moreover without any symmetry assumption the global existence of smooth solutions near a given constant steady state for both compressible navier stokes poisson and euler poisson equations on an exterior domain in r 3 with physical boundary conditions is also established with the exponential stability a key issue addressed in this paper is on the global in time regularity of solutions near physical boundaries this is in particular so for the 3 d compressible navier stokes poisson equations to which global smooth solutions of initial boundary value problems are seldom found in literature to the best of knowledge

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

strichartz estimates and moment bounds for the relativistic vlasov maxwell system we consider the relativistic vlasov maxwell system with data of unrestricted size and without compact support in momentum space in the two dimensional and the two and a half dimensional cases glassey schaeffer proved commun math phys 185 257 284 1997 arch ration mech anal 141 331 354 1998 arch ration mech anal 141 355 374 1998 that for regular initial data with compact momentum support this system has unique global in time classical solutions in this work we do not assume compact momentum support for the initial data and instead require only that the data have polynomial decay in momentum space in the two dimensional and the two and a half dimensional cases we prove the global existence uniqueness and regularity for solutions arising from this class of initial data to this end we use strichartz estimates and prove that suitable moments of the solution remain bounded moreover we obtain a slight improvement of the temporal growth of the l infty x norms of the electromagnetic fields compared to glassey and schaeffer commun math phys 185 257 284 1997 arch ration mech anal 141 355 374 1998 in the three dimensional case we apply strichartz estimates and moment bounds to show that a regular solution can be extended as long as p 0 theta f l q x l 1 p remains bounded for theta frac 2 q 2 q leqq infty this improves previous results of pallard indiana univ math j 54 5 1395 1409 2005 commun math sci 13 2 347 354 2015

asymptotic behavior of weak solutions for the relativistic vlasov maxwell equations with large light speed abstract we study here the behavior of time periodic weak solutions for the relativistic vlasov maxwell boundary value problem in a three dimensional bounded domain with strictly star shaped boundary when the light speed becomes infinite we prove the convergence toward a time periodic weak solution for the classical vlasov poisson equations

on the classical solutions to the hydrodynamic model for semiconductors abstract this paper mainly deals with the multidimensional hydrodynamic model for semiconductors inspired by the previous papers y shizuta s kawashima systems of equations of hyperbolic parabolic type with applications to the discrete boltzmann equation hokkaido math j 14 1985 249 275 s kawashima w a yong dissipative structure and entropy for hyperbolic systems of balance laws arch ration mech anal 174 2004 345 364 w a yong entropy and global existence for hyperbolic balance laws arch ration mech anal 172 2004 247 266 we develop some new frequency localization estimates to establish the global existence and exponential stability of small classical solutions in a class of critical besov spaces which are different from estimates in our recent paper d y fang j xu t zhang global exponential stability of classical solutions to the hydrodynamic model for semiconductors math models methods appl sci 17 2007 1507 1530 furthermore this new method can also be applied to the multidimensional euler equations with damping the analytic tool used is the littlewood paley decomposition

on a periodic schrodinger equation with nonlocal superlinear part we consider the choquard pekar equation open image in new window and focus on the case of periodic potential v for a large class of even functions w we show existence and multiplicity of solutions essentially the conditions are that 0 is not in the spectrum of the linear part v and that w does not change sign our results carry over to more general nonlinear terms in arbitrary space dimension n 2

comparison of various means for operators for hilbert space operatorsh k xwithh k 0 the norm inequality h1 2xk1 2 12 hx xk is known where is an arbitrary unitarily invariant norm a refinement of this arithmetic geometric mean inequality is studied similar norm inequalities are indeed established for various natural means for operators such as the logarithmic mean

large time behavior of euler poisson equations for isothermal fluids with spherical symmetry abstract in this paper the large time behavior of spherically symmetric weak solutions to the multi dimensional isothermal euler poisson system in an annulus is considered when space dimension n 2 it is shown that the weak solutions converge to the unique stationary solution exponentially in time no smallness and regularity conditions are assumed

asymptotic convergence to planar stationary waves for multi dimensional unipolar hydrodynamic model of semiconductors abstract in this study we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of euler poisson equations based on the results that we have obtained in the first part huang et al 2011 16 for the 1 d case we can further show the stability of planar stationary waves in multi dimensional case utilizing the energy method we obtain the global existence of the solutions of high dimensional euler poisson equations for the unipolar hydrodynamic model and prove that the solutions converge to the planar stationary waves time exponentially

convergence of the nonisentropic euler poisson equations to incompressible type euler equations abstract in this paper we investigate a multidimensional nonisentropic hydrodynamic euler poisson model for semiconductors we study the convergence of the nonisentropic euler poisson equation to the incompressible nonisentropic euler type equation via the quasi neutral limit the local existence of smooth solutions to the limit equations is proved by an iterative scheme the method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit

a complete refinement of young s inequality abstract in this article we present multiple term refinements of young s inequality for real numbers and operators in particular given a natural number n we find n positive terms refining young s inequality detailed properties of this refinement are studied leading to a new interesting mean

global classical solutions to the 3d nordstrom vlasov system the nordstrom vlasov system describes the kinetic evolution of self gravitating collisionless matter in the framework of a relativistic scalar theory of gravitation we prove global existence and uniqueness of classical solutions for the corresponding initial value problem in three dimensions when the initial data for the scalar field are smooth and the initial particle density is smooth with compact support

an improved local blow up condition for euler poisson equations with attractive forcing abstract we improve the recent result of chae and tadmor 2008 10 proving a one sided threshold condition which leads to a finite time breakdown of the euler poisson equations in arbitrary dimension n

the hasegawa petz mean properties and inequalities abstract we study a family of means introduced by h hasegawa and d petz 1996 13 properties with respect to the parameter such as monotonicity and logarithmic concavity further monotonicity and concavity in the mean variables are shown besides the comparison between the hasegawa petz mean and the geometric mean is completely solved the connection to earlier results on operator monotonicity and some applications are also discussed

completely positive mappings and mean matrices abstract some functions f r r induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices moreover such a function f can define a linear mapping j d f 1 m n m n on matrices which is basic in the constructions of monotone metrics the present subject is to check the complete positivity of j d f 1 in the case of a few concrete functions f this problem has been motivated by applications in quantum information

asymptotic profile in a one dimensional steady state nonisentropic hydrodynamic model for semiconductors we study the stationary flow for a one dimensional nonisentropic hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron density the electron current density and electron temperature coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we show the strong convergence of the sequence of solutions and give the associated convergence rate

global existence and large time behavior of weak solutions to the compressible magnetohydrodynamic equations with coulomb force abstract in this paper we consider the equations of magnetohydrodynamics with coulomb force which is of hyperbolic parabolic elliptic mixed type by constructing the approximate solutions to the modified system with an artificial pressure term added global existence of finite energy weak solutions is established via the weak convergence method more careful argument has been paid to overcome the new difficulty arising from the poisson term of coulomb force in two dimensions when the adiabatic exponent is close to one we also investigate the large time behavior of such weak solutions after discussing the regularity and uniqueness of solutions to the stationary problem