blow up of solutions to 1 d euler equations with time dependent damping abstract we study the 1 d isentropic euler equations with time dependent damping t x u 0 t u x u 2 x p 1 t u t 0 1 e 0 x u t 0 e u 0 x in a previous paper 8 we have proven that when 1 2 the 1 d euler equations have global existence of small data solutions however in this paper we will show that when the damping with respect to time decays faster or equal to 2 1 t the c 1 solution of the above system will blow up in finite time more precisely when 1 0 2 or 1 0 we will give a finite upper bound for the lifespan combining the results in this paper and 8 we see that when the damping decays with time like 1 t the critical exponents for to separate the global existence and finite time blow up of small data solutions are 1 2

on the covering number of a matroid element abstract let s be a nonempty finite set with cardinality m let m s i m be a matroid on s with no loops we present results connecting the structure of the bases of m k the k th power of m and the covering number of elements of s in m

the pointwise estimates of solutions for a model system of the radiating gas in multi dimensions in this paper we study the time asymptotic behavior of solutions for a hyperbolic elliptic coupled system known as a model system of the radiating gas in rn when the initial perturbation corresponding to a positive constant state is sufficiently small in hs rn the global existence and pointwise estimates of the solution are obtained by using the method of the green function combined with some energy estimates furthermore we obtain the lp 1 p convergence rate of the solution

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

best asymptotic profile for linear damped p system with boundary effect abstract this paper is devoted to the study of the 2 2 linear damped p system with boundary effect by a heuristic analysis we realize that the best asymptotic profile for the original solution is the parabolic solution of the ibvp for the corresponding porous media equation with a specified initial data in particular we further show the convergence rates of the original solution to its best asymptotic profile which are much better than the existing rates obtained in the previous works the approach adopted in the paper is the elementary weighted energy method with green function method together

existence and stability of planar diffusion waves for 2 d euler equations with damping abstract to study the non linear stability of a non trivial profile for a multi dimensional systems of gas dynamics the combination of the green function on estimating the lower order derivatives and the energy method for the higher order derivatives is shown to be not only useful but sometimes maybe also essential in this paper we study the stability of a planar diffusion wave for the isentropic euler equations with damping in two dimensional space by introducing an approximate green function for the linearized equations around the planar diffusion wave and by applying the energy method we prove the global existence and the l 2 convergence rate of the solution when the initial data is a small perturbation of the planar diffusion wave the decay rates of the perturbation and its lower order spatial derivatives obtained are optimal in the l 2 norm furthermore the constructed approximate green function in this paper can be used for the pointwise and the l p estimates of the solutions concerned in fact the approach by combining of the green function and energy method can be applied to other system especially when the derivatives of the coefficients in the system have certain time decay properties

convergence to nonlinear diffusion waves for solutions of euler equations with time depending damping abstract in this paper we are concerned with the asymptotic behavior of solutions to the system of euler equations with time depending damping in particular include the constant coefficient damping we rigorously prove that the solutions time asymptotically converge to the diffusion wave whose profile is self similar solution to the corresponding parabolic equation which justifies darcy s law compared with previous results about euler equations with constant coefficient damping obtained by hsiao and liu 1992 2 and nishihara 1996 9 we obtain a general result when the initial perturbation belongs to the same space i e h 3 r h 2 r our proof is based on the classical energy method

convergence to nonlinear diffusion waves for solutions of p system with time dependent damping abstract in this paper we study the cauchy problem for the hyperbolic p system with time gradually degenerate damping term 1 1 t u for 0 1 and show that the damped p system has a couple of global solutions uniquely and such solutions tend time asymptotically to the shifted nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation governed by the darcy s law we further derive the convergence rates when the initial perturbations are in l 2 the approach adopted is the technical time weighted energy method

conditions for a symmetrized decomposable tensor to be zero let x1ast xm be a decomposable symmetrized tensor corresponding to the symmetric group sm and an irreducible character a necessary and sufficient condition on the vectors x1 xm is given for x1 xm to be zero

wave front tracing and asymptotic stability of planar travelling waves for a two dimensional shallow river model abstract the propagation of surface water waves in a frictional channel with a uniformly inclined bed is governed by a two dimensional shallow river model in this paper we consider the time asymptotic stability of weak planar travelling waves for a two dimensional shallow river model with darcy s law we derive an effective parabolic equation to analyze the wave front motion by employing weighted energy estimates we show that weak planar travelling waves are time asymptotically stable under sufficiently small perturbations

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation we study gas flow in vibrational nonequilibrium the model is a 4 4 nonlinear hyperbolic system with relaxation under physical assumptions properties of thermodynamic variables relevant to stability are obtained global existence for cauchy problems with smooth and small data is established and large time behavior is studied in the pointwise sense we formulate the fundamental solution in a systematic way for a general linear system with relaxation the fundamental solution provides insights to the behavior of the nonlinear system and is crucial to obtain our pointwise asymptotic picture for the nonequilibrium flow we also clarify in a general setting the relation between subcharacteristic conditions and a dissipative criterion that was originally proposed for hyperbolic parabolic systems and has now proved to be important also for hyperbolic systems with relaxation

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

stability of viscous scalar shock fronts in several dimensions we prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions the proof uses the integrated equation and an effective equation for the motion of the front itself we derive energy estimates that balance terms from the integrated equation with terms from the front motion equation in this paper we prove that viscous shock profiles for scalar conservation laws are stable in two or more space dimensions these multidimensional stability questions are separate from their one dimensional analogues because of the possibility of transverse instabilities such as those that occur in combustion fronts lu and in shock waves with phase changes the proof here is a rigorous version of arguments that are used to derive effective equations such as the kuramoto sivashinsky equation to describe the behavior of fronts the one dimensional stability for scalar conservation laws was proven by ii in and oleinik io using the integrated equation see below and a max imum principle another proof based on weighted norms and spectral theory for the linearized problem was given by sattinger s the multidimensional stability proof below has more in common with the stability proofs for systems of conservation laws in one space dimension begun by kawashima and mat sumura km and goodman go and completed by liu li these proofs use l2 energy estimates for the integrated equation we consider equations of the form ut f u x g u y uxx uyy where f u is a strictly convex function of u

flags and equality of tensors abstract we state a necessary and sufficient condition for equality of decomposable symmetrized tensors when the symmetrizer is associated to an irreducible character of s p corresponding to the partition of p and the tensors are the images by this symmetrizer of the tensor product of a family of vectors of rank partition we make an application of this result to the representation of flags by projective points

diffusive relaxation limit of classical solutions to the damped compressible euler equations abstract we construct uniform global classical solutions to the damped compressible euler equations on the framework of general besov spaces which includes both the usual sobolev spaces h s r d s 1 d 2 and the critical besov space b 2 1 1 d 2 r d such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous chemin lerner spaces furthermore we obtain the diffusive relaxation limit of euler equations towards the porous medium equation by means of aubin lions compactness argument

l p convergence rates of planar waves for multi dimensional euler equations with damping abstract in this paper the l p convergence rates of planar diffusion waves for multi dimensional euler equations with damping are considered the analysis relies on a newly introduced frequency decomposition and green function based energy method it is a combination of the l p estimate on the low frequency component by using an approximate green function and l 2 estimate on the high frequency component through the energy method by noticing that the low frequency component in the approximate green function has the algebraic decay which governs the large time behavior while the high frequency component has the exponential decay but with singularity their combination leads to a global algebraic decay estimate to use the decay property only of the low frequency component in the approximate green function avoids the singularity in the high frequency component so that it simplifies and improves the previous works on this system this new approach of the combination of the green function and energy method through the frequency decomposition can also be applied to the hyperbolic parabolic systems satisfying the kawashima condition and also the systems whose derivatives of the coefficients have suitable time decay properties

global solution and large time behavior of the 3d compressible euler equations with damping national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

initial boundary value problem for p system with damping in half space abstract in this paper the initial boundary value problem for p system with damping in half space is studied with a posed mix boundary condition the fundamental solution green s function for cauchy problem is constructed with a sharp decaying structure and a precise capture of the singularity by a singularity removal process later the symbols of both fundamental solution and green s function for initial boundary value problem are obtained with transformed variable s and spatial variable x while in this level the green s function could be decomposed into fundamental solution and boundary operator thus with the study of boundary operator and previous precise information about the fundamental solution the pointwise structure as well as the singular structure of the green s function is established finally the nonlinear stability is obtained by the green s function and a priori estimate from energy method

on the powers of a vectorial matroid an equivalence relation abstract let v be a nonzero vector space over the field f of characteristic zero let x be a finite family of nonzero vectors of v for each a v we denote by ma the vectorial matroid of x a for each k n we denote by ma k the kth power of ma we define an equivalence relation k on v such that a kb if and only if the matroids ma k and mb k are on the same set and have the same set of independent sets we present results on this equivalence relation

asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping ii this paper as a follow up to the recent work of k nishihara 1997 j differential equations133 384 395 is concerned with the asymptotic behaviors of the solution of quasilinear hyperbolic equation with linear damping vtt a vx x vt 0 a v 0forallv r which satisfies the following prescribed initial condition v t x vt t x t 0 v0 x v1 x x r compared with the results obtained by k nishihara the main novelties of our present paper lie in the following first we recover all the results obtained by k nishihara under some other smallness assumptions on the initial data v0 x v1 x which are much weaker than those needed in k nishihara s arguments second under some additional assumptions on the nonlinear function a v and on the initial data v0 x v1 x when 0 0 1 0 we succeed in proving that t x is still an asymptotic profile of v t x and this answers partially the open problem left by k nishihara

pointwise estimates and lp convergence rates to diffusion waves for p system with damping abstract by introducing a new approximate green function we obtain the pointwise estimates on the solutions of euler equations with linear frictional damping from which we can deduce the optimal l p 1 p convergence rates to the nonlinear diffusion waves the pointwise estimates and l p 1 p convergence rates given in this paper are new

convergence to equilibrium in wasserstein distance for damped euler equations with interaction forces we develop tools to construct lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped euler system under the influence of external and interaction potential forces with respect to the 2 wasserstein distance we also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2 wasserstein distance and provide rigorous proofs for particular examples in one spatial dimension

the decay rate of solution for the bipolar navier stokes poisson system in this paper the cauchy problem for the bipolar navier stokes poisson system is studied we obtain the global existence and the hs decay rate of classical solutions for this problem our approach is mainly based on the analysis of the green s function of the linearized system and some elaborate energy estimates it should be mentioned that with the help of long wave short wave decomposition the decay rate of the higher order derivatives of the solutions is obtained furthermore based on the hs decay rate of the solutions we also give the lp estimate of the solution

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

half space problem for euler equations with damping in 3 d abstract in this paper we consider the half space problem for euler equations with damping in 3 d we restudy the fundamental solution for the cauchy problem to obtain an exponentially sharp pointwise structure and a clear decomposition of the singular regular components later both green s function for initial boundary value problem and fundamental solutions for cauchy problems are investigated in the transformed domain after laplace transform the symbols are obtained and a connection between green s function and fundamental solutions are established for the pointwise space time structure of green s function finally the sharp estimates for green s function together with a priori estimates from the energy method for high order derivatives result in the nonlinear stability of the solution and also the decaying rates

the chern simons action in noncommutative geometry a general definition of chern simons actions in noncommutative geometry is proposed and illustrated in several examples these examples are based on space times which are products of even dimensional riemannian spin manifolds by a discrete two point set if the algebras of operators describing the noncommutative spaces are generated by functions over such space times with values in certain clifford algebras the chern simons actions turn out to be the actions of topological gravity on the even dimensional spin manifolds by constraining the space of field configurations in these examples in an appropriate manner one is able to extract dynamical actions from chern simons actions

l p convergence rates of solutions for n dimensional quasilinear damped wave equation we realize the asymptotic profile for the solutions to the n dimensional quasilinear damped wave equation in the divergence form is the solution of the corresponding linear parabolic equation with special initial data and we further show the lp 1 p infinity in particular p 1 convergence rates to this linear asymptotic profile c 2013 elsevier inc all rights reserved

large time behavior for the system of compressible adiabatic flow through porous media in r3 abstract the cauchy problem of the system of compressible adiabatic flow through porous media in r 3 is considered we obtain the global existence and large time behavior of the solution when the initial data is close to its equilibrium in h 3 norm this is a continuing work of 31 where due to non dissipative property of the entropy s an additional assumption that the initial data is bounded in l 1 norm plays a key role in closing the a priori energy estimates and hence establishing the global existence of the solution in this paper to remove this assumption we first decompose the solution u into high frequency part u h and low frequency part u l then by constructing delicate energy functionals for u h and optimal decay rates for u l we can get the desired energy estimates to close the a priori assumption furthermore we get the optimal l 2 l 2 decay rate of the solution and show that the velocity decays faster than the density

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

convergence to strong nonlinear diffusion waves for solutions of p system with damping this paper is concerned with the p system with frictional damping and our main purpose is two fold first we show that for a certain class of given large initial data nu 0 x u 0 x the cauchy problem 1 1 1 2 admits a unique global smooth solution nu t x u t x and such a solution tends time asymptotically at the optimal l p 2 less than or equal to p less than or equal to infinity decay rates to the corresponding nonlinear diffusion wave over bar t x u over bar t x governed by the classical darcy s law provided that the corresponding prescribed initial error function v 0 x u 0 x ties in h 3 x h 2 r boolean and l 1 x l 1 r compared with former results in this direction obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 k nishihara 1996 j differential equations 131 171 188 and k nishihara w k wang and t yang 2000 j differential equations 161 191 218 our main novelty lies in the facts that the nonlinear diffusion wave over bar t x u over bar t x need not to be weak and v 0 x u 0 x can be chosen arbitrarily large secondly we show that the nonlinear diffusion waves over bar t x u over bar t x are nonlinear stable provided that the strength or the nonlinear diffusion waves is weak and that the initial disturbance v 0 x u 0 x satisfies the assumption that parallel tov 0xx x parallel to l infinity parallel tou 0x x parallel to l infinity is sufficiently small we also show that the smallness assumption imposed oil the strength of the diffusion waves is a necessary condition to guarantee the nonlinear stability result and compared with the corresponding results obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 the smallness conditions we imposed on the initial disturbance are much more weaker c 2001 academic press

new conditions for equality of decomposable symmetrized tensors we determine conditions for equality of decomposable symmetrized tensors in arbitrary symmetry classes based on these conditions we derive results for equality of decomposable symmetrized tensors associated to certain special group characters

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

gravity in non commutative geometry we study general relativity in the framework of non commutative differential geometry as a prerequisite we develop the basic notions of non commutative riemannian geometry including analogues of riemannian metric curvature and scalar curvature this enables us to introduce a generalized einstein hilbert action for non commutative riemannian spaces as an example we study a space time which is the product of a four dimensional manifold by a two point space using the tools of non commutative riemannian geometry and derive its generalized einstein hilbert action in the simplest situation where the riemannian metric is taken to be the same on the two copies of the manifold one obtains a model of a scalar field coupled to einstein gravity this field is geometrically interpreted as describing the distance between the two points in the internal space

pointwise time asymptotic behavior of solutions to a general class of hyperbolic balance laws abstract in this paper we are interested in a general class of hyperbolic balance laws within the frame work of existence of a convex entropy function that symmetrizes the system in certain sense and the kawashima shizuta condition we study the large time behavior of the solution to the cauchy problem in one space dimension for a solution around a constant equilibrium state we predetermine the asymptotic solution as a superposition of the constant state and diffusion waves along the equilibrium characteristic directions we estimate the remainder in the pointwise sense both in space and in time the decay rates in various directions are optimal which further give the optimal l p rates with 1 p applications to several examples including the kerr debye model are given

global existence of solutions to 1 d euler equations with time dependent damping abstract in this paper we study the 1 d isentropic euler equations with time dependent damping our damping decays at a speed of order 1 with respect to time which is a little weaker than the linear one under our assumption we will prove the global existence of solutions to the euler system and obtain l 2 and l estimates for the solutions our approach is based on some detailed energy estimates

asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping we consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear dampingvtt a vx x vt 0 x t r 0 subsequent to k nishihara j differential equations131 1996 171 188 in that article the system with dampingvt ux 0 ut p v x u p v 0 was treated and the convergence rates to the diffusion wave by l hsiao and t p liu comm math phys 143 1992 599 605 and l hsiao and t p liu chinese ann math ser b14 1993 465 480 were improved for initial data v0 u0 x satisfying v0 u0 v0 0 and v0 x v0 dx 0 this system is reduced to the quasilinear hyperbolic equation with linear dampingvtt p v0 vx p v0 x vt 0 and the decay rates v t l o t 1 2 vx t l o t 1 vt t l o t 3 2 were obtained provided that v vt t 0 h3 h2 is small and inl1 l1 from these decay rates vis expected to behave as a solution to the parabolic equation the aims of this paper are to seek the asymptotic profile x t satisfying t l o t 1 2 x t l o t 1 t t l o t 3 2 and to show that the solution of satisfies v t l o t 1 v x t l o t 3 2 v t t l o t 2 the proof is based on the elementary energy method and the green function method for the parabolic equation

asymptotic behavior of solutions to bipolar euler poisson equations with time dependent damping abstract in this paper we study the one dimensional euler poisson equations of bipolar hydrodynamic model for semiconductor device with time dependent damping effect j 1 t for 1 1 where the damping effect is time gradually degenerate for 0 and time gradually enhancing for 0 such a damping effect makes the hydrodynamic system possess the nonlinear diffusion phenomena time asymptotic weakly or strongly based on technical observation and by using the time weighted energy method where the weights are artfully chosen we prove that the system admits a unique global smooth solution which time asymptotically converges to the corresponding diffusion wave when the initial perturbation around the diffusion wave is small enough the convergence rates are specified in the algebraic forms o t 3 4 1 and o t 1 according to different values of in 1 1 7 and 1 7 1 respectively where 1 7 is the critical point and the convergence rate at the critical point is o t 6 7 ln t all these convergence rates obtained in different cases are optimal in the sense when the initial perturbations are l 2 integrable particularly when 1 7 the convergence rate is the fastest namely the asymptotic profile of the original system at the critical point is the best

on the kernel of the derivation operator abstract we state a necessary and sufficient condition for a symmetrized tensor to belong to the kernel of the derivation operator the derivation operator a generalization of the associated transformation introduced by m marcus in o shisha ed inequalities ii academic press new york 1970 p 223 is a linear operator on the range of the symmetrizer when the symmetrizer is associated to an absolutely irreducible character of s m corresponding to the partition of m and the tensor is the image by this symmetrizer of the tensor product of a family of vectors of rank partition

pointwise convergence to shock waves for viscous conservation laws we are interested in the pointwise behavior of the perturbations of shock waves for viscous conservation laws it is shown that besides a translation of the shock waves and of linear and nonlinear diffusion waves of heat and burgers equations a perturbation also gives rise to algebraically decaying terms which measure the coupling of waves of different characteristic families our technique is a combination of time asymptotic expansion construction of approximate green functions and analysis of nonlinear wave interactions the pointwise estimates yield optimal lp convergence of the perturbation to the shock and diffusion waves 1 p the new approach of obtaining pointwise estimates based on the green functions for the linearized system and the analysis of nonlinear wave interactions is also useful for studying the stability of waves of distinct types and nonclassical shocks these are being explored elsewhere 1997 john wiley sons inc

the covering number of elements of a matroid and associated transformations abstract let s be a nonempty finite set with cardinality m let m s i m be a matroid on s let x be an element of s which is not a loop of m the covering number of x in m is the smallest positive integer s such that x is a coloop of the union of s copies of m we investigate relations between the covering number of the elements in m and in its minors applications to the study of the rank partition and associated transformation are presented

asymptotic behavior for scalar viscous conservation laws with boundary effect abstract we consider the asymptotic stability of viscous shock wave for scalar viscous conservation lawsut f u x uxxon the half space 0 with boundary valuesu x u u x 0 u our problem is divided into three cases depending on the sign of shock speedsof the shock u u whens 0 the asymptotic state ofubecomes d t whered t depends implicitly on the initial datau x 0 and is related to the boundary layer of the solution at the boundaryx 0 the stability of this state fors 0 is also treated

the covering number of the elements of a matroid and generalized matrix functions abstract let s be a nonempty finite set with cardinality m let m be a matroid on s with no loops the covering number of an element x in s is the smallest positive integer k such that x is a coloop of the union of k copies of m we investigate connections between the structure of m and the values of the covering numbers of elements of s applications to the study of the rank partition and generalized matrix functions are presented

induced qcd from the noncommutative geometry of a supermanifold the noncommutative geometry of a two leaf parisi sourlas supermanifold in connes formalism using different k cycles over the grassmann algebra valued functions on the supermanifold is studied we find that the curvature of the trivial noncommutative vector bundle defines in the simplest case the super yang mills action coupled to a scalar field by considering a modified dirac operator and a suitable limit of its parameters we then obtain an action that turns out to be the continuum limit of the induced qcd in the kazakov migdal model

half space problem of the system of compressible adiabatic flow through porous media in multi d abstract in this paper we consider the half space problem for the system of compressible adiabatic flow through porous media in 2 d and 3 d combining energy method green s function method and bootstrap method one establishes the decaying energy estimates which lead to global existence and optimal l 2 decaying rate of the solution finally for more large time information especially in spatial variables one applies green s function solution representation obtained by duhamel s principle and a priori estimate from energy method to obtain the space time pointwise structure of the solution

nonlinear diffusion waves for hyperbolic p system with nonlinear damping abstract this paper is concerned with the p system of hyperbolic conservation laws with nonlinear damping when the constant states are small the solutions of the cauchy problem for the damped p system globally exist and converge to their corresponding nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation given by the darcy s law the optimal convergence rates are also obtained in order to overcome the difficulty caused by the nonlinear damping a couple of correction functions have been technically constructed the approach adopted is the elementary energy method together with the technique of approximating green function on the other hand when the constant states are large the solutions of the cauchy problem for the p system will blow up at a finite time

asymptotic stability of solutions to the hamilton jacobi equation abstract this paper is concerned with the asymptotic behavior of the solution for the generalized hamilton jacobi equation u t f d u u it is known that one dimensional equation v t c 0 v x 2 v x x has a self similar solution v x 1 t if v v where v v t v v t this kind of solution is called planar diffusion wave in multi dimension m d in this paper it is shown that under some smallness conditions the solutions to the generalized hamilton jacobi equation converge to the above diffusion wave v x 1 t with c 0 1 2 2 f 1 2 n 1 2 1 0 as time tends to infinity the convergence rate in time is also obtained

quantum k theory i the chern character we construct a cocycle on an infinite dimensional generalization of ap summable fredholm module our framework is related to connes cyclic cohomology and is motivated by our work on index theory on infinite dimensional manifolds thep summability condition is characteristic of dimensiono p we replace this assumption by the requirement that there exists an underlying heat kernel which is trace class then we use the heat kernel to regularize states in dimension independent fashion our cocycle may be interpreted as an infinite dimensional chern character