rescaling invariance and anomalous transport in a stochastic layer the anomalous chaotic transport in a one degree of freedom hamiltonian system subjected to a small time periodic perturbation is investigated strong quasiperiodic dependencies of the statistical properties of the motion on log epsilon are found where epsilon is a perturbation parameter the period log lambda depends on the rescaling parameter lambda which is determined only by the frequency of perturbation and behavior of unperturbed hamiltonian near a saddle point the results confirm and generalize a recently established new universal rescaling property of perturbed motion near a saddle point

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

the distance between two separating reducing slopes is at most 4 let m be a simple 3 manifold such that one component of m say f has genus at least two for a slope on f we denote by m the manifold obtained by attaching a 2 handle to m along a regular neighborhood of on f if m is reducible then is called a reducing slope in this paper we shall prove that the distance between two separating reducing slopes on f is at most 4

reducible and reducible handle additions let m be a simple 3 manifold with f a component of m of genus at least two for a slope on f we denote by m a the manifold obtained by attaching a 2 handle to m along a regular neighborhood of a on f suppose that a and are two separating slopes on f such that m a and m are reducible then the distance between a and is at most 2 as a corollary if g f 2 then there is at most one separating slope on f such that m is either reducible or reducible

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

some new aspects of levy walks and flights directed transport manipulation through flights and population exchange levy flights and walks have been shown to arise in a broad spectrum of areas leading to anomalous diffusion here we investigate their central role in some dynamical phenomena encountered in hamiltonian systems with a mixed phase space in particular we discuss within the continuous time random walk ctrw framework the possibility to obtain currents in hamiltonian systems and how to manipulate them and the effect of population exchange between islands of stability the latter can be viewed as the classical counterpart of chaos assisted tunneling

frequency localization duhamel principle and its application to the optimal decay of dissipative systems in low dimensions abstract recently a time decay framework l 2 r n b 2 s r n s 0 has been given by 49 for linearized dissipative hyperbolic systems which allows to pay less attention to the traditional spectral analysis however owing to interpolation techniques those decay results for nonlinear hyperbolic systems hold true only in higher dimensions n 3 and the analysis in low dimensions say n 1 2 was left open we try to give a satisfactory answer in the current work first of all we develop new time decay properties on the frequency localization duhamel principle and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n 1 2 by using a new technique which is the so called piecewise duhamel principle in localized time weighted energy approaches compared to 49 finally as direct applications explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure for instance damped compressible euler equations the thermoelasticity with second sound and timoshenko systems with equal wave speeds

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

decay property of regularity loss type for nonlinear hyperbolic elliptic system in multi dimensions abstract in this paper we study the asymptotic behavior of solutions for a hyperbolic elliptic system with a 2m order elliptic part in multi dimensional space this system is a modified version of the simplest radiating gas model and it verifies l p decay property of regularity loss type in r n the global existence and l p estimates of the solution to the cauchy problem for the hyperbolic elliptic system are obtained since the dissipative property of this system is so weak in high frequency region the usual energy method does not work well in deriving the a priori estimates for global solutions to the nonlinear problem our analysis is based on a frequency decomposition and the method of combining the green function with some time weight energy estimates

the pointwise estimates to solutions for 1 dimensional linear thermoelastic system with second sound in this paper we study the thermoelastic system with second sound in one space variable the mathematical model is a hyperbolic partial differential system with damping term which brings about some parabolic properties the pointwise estimates of the solution are obtained and from which the generalized huygens principle is shown our approach is based on detailed analysis on the green function of the system

global existence and asymptotic behavior of the solutions to the three dimensional bipolar euler poisson systems abstract in this paper the global existence of smooth solutions for the three dimensional bipolar hydrodynamic model is studied when the initial data are close to a constant state the l 2 decay rate of the solutions is also obtained our approach is based on the detailed analysis of the green function of the linearized system and the elaborate energy estimates as far as we known it is the first result about the existence and l 2 decay rate of global smooth solutions to the multi dimensional bipolar hydrodynamic model

scaling invariance of the diffusion coefficient in a family of two dimensional hamiltonian mappings departamento de fisica unesp universidade estadual paulista avenida 24a 1515 13506 900 rio claro sao paulo

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

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

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

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

large time behavior of solutions for compressible euler equations with damping in r 3 we consider the long time behavior and optimal decay rates of global strong solutions for the isentropic compressible euler equations with damping in r3 in the present paper when the regular initial data belong to some sobolev space hl r3 b 1 s r3 with l 4 and s 0 1 we show that the density of the system converges to its equilibrium state at the rates 1 t 34 s2 in the l2 norm or 1 t 32 s2 in the l norm respectively the momentum of the system decays at the rates 1 t 54 s2 in the l2 norm or 1 t 2 s2 in the l norm respectively which are shown to be optimal for the compressible euler equations with damping

canonical maps near separatrix in hamiltonian systems a systematic and rigorous method to construct symplectic maps near separatrix of generic hamiltonian systems subjected to time periodic perturbations is developed it is based on the method of canonical transformation of variables to construct hamiltonian maps j phys a 35 2811 2002 using canonical transformation of variables and the first order approximation for the generating function the general form of mapping in terms of time and energy variables is obtained different limiting cases of the mapping are considered the method is illustrated for simple hamiltonian systems with one and a large number of saddle points it is also applied to derive mappings for the periodic driven morse oscillator describing the process of stochastic excitation and dissociation of diatomic molecules the so called canonical kepler map is derived for the one dimensional hydrogen atom in a microwave field

the lp decay estimates for the chemotaxis shallow water system abstract in this paper we consider the large time behavior of solution for the chemotaxis shallow water system in two dimension by the method of frequency decomposition first we construct the green s function of the linearized system and get the corresponding estimates for low frequency part then we introduce an energy method we named double cycle method to get the decay rate for high frequency part due to the dissipative mechanism of this system the high frequency part decays faster than the low frequency part

pointwise estimates of solution for the navier stokes poisson equations in multi dimensions abstract the cauchy problem of the navier stokes poisson equations in multi dimensions n 3 is considered we obtain the pointwise estimates of the solution when it is a perturbation of the constant state then we have the optimal l p r n p 1 convergence rate of the solution

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

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

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

global solution to initial boundary value problem for gas dynamics in thermal nonequilibrium abstract the global existence and long time behavior of smooth solutions to an initial boundary value problem for the system of thermal nonequilibrium gas dynamics are studied in this paper

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

pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions abstract in this paper we study the pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions by the green function method furthermore we obtain the l p convergence rate of the solution

large time behavior of solutions for the nonlinear wave equation with viscosity in odd dimensions abstract we study the dissipation of solutions of the cauchy problem for the nonlinear dissipative wave equation in odd multi spatial dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygens 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

global well posedness for systems of hyperbolic parabolic composite type with center manifold abstract concerning the global existence of classical solution to systems of hyperbolic parabolic composite type a well known general theory was established by kawashima in 4 where the dissipation condition kawashima shizuta condition to the linearized system plays a fundamental role recently systems with much weaker dissipations have attracted a lot of attentions see 1 2 10 11 among others the typical feature of this kind of system is that the corresponding linearized system has one eigenvalue with the real part equals to zero this violates the kawashima shizuta stability conditions in this paper we develop a general global well posedness theory for this kind of system moreover as the applications of the general theory several examples are given

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

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

asymptotic behavior of solutions to conservation laws with diffusion type terms of regularity gain and regularity loss abstract in this paper we study asymptotic behaviors of solutions to the cauchy problem of nonlinear conservation laws with a diffusion type source term related to an index s r for s 1 and s 1 the diffusion type term takes on a characteristic of regularity gain and regularity loss on the high frequency domain respectively by combining the green function method with the energy method we overcome the weakly dissipative structure of the equation for the case of s 1 and obtain the global existence and optimal l p norm time decay rates of solutions in the case of regularity gain pointwise estimates of solutions are shown by using the refined analysis on the green function

pointwise estimates of global small solutions to the generalized double dispersion equation abstract in this paper we investigate the initial value problem for the generalized double dispersion equation in r n under suitable conditions global classical solutions are proved for n 3 and n 1 respectively moreover pointwise estimates of global classical solutions are established when n 3 and n is an odd integer by fourier splitting frequency technique

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

only single twists on unknots can produce composite knots let k be a knot in the 3 sphere s3 and d a disc in s3 meeting k transversely more than once in the interior for non triviality we assume that ik n di 2 over all isotopy of k let kn c s3 be a knot obtained from k by cutting and n twisting along the disc d or equivalently performing 1 n dehn surgery on od then we prove the following 1 if k is a trivial knot and kn is a composite knot then inj 1 2 if k is a composite knot without locally knotted arc in s3 od and kn is also a composite knot then inj 2 we exhibit some examples which demonstrate that both results are sharp independently chaim goodman strauss has obtained similar results in a quite different method

large time behavior for the solution to the generalized benjamin bona mahony burgers equation with large initial data in the whole space abstract in this paper we consider the global existence as well as the optimal decay estimates of the cauchy problem for the multi dimensional benjamin bona mahony burgers equation with large initial data in the whole space and these results are obtained by green s function method fourier analysis method energy estimates method combined with the time frequency decomposition method

large time behavior of solutions for hyperbolic balance laws we study the existence and the large time behavior of global solutions to the initial value problem for hyperbolic balance laws in n space dimensions with n 3 admitting an entropy and satisfying the stable condition we first construct global existence of the solutions to such a system around a steady state if the initial energy is small enough then we show that k order derivatives of these solutions approach a constant state in the lp norm at a rate o t 12 k n2 np with p 2 and 0 n2 provided that initially z0 b 2 where b 2 is a homogeneous besov space these decay results do not impose an additional smallness assumption on lp norm of the initial data and we thus improve the results in 3 19 we also show faster decay results in the sense that if pz0 b 2 i p z0 b 2 1 with n2 n 22 k order derivatives of the solutions approach a constant state in the lp norm at a rate o t 12 k 1 n2 np