optimal gradient estimates and asymptotic behaviour for the vlasov poisson system with small initial data the vlasov poisson system describes interacting systems of collisionless particles for solutions with small initial data in three dimensions it is known that the spatial density of particles decays as t 3 at late times in this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so that in n dimensions for n geqq 3 the derivative of the density of order k decays as t n k an asymptotic formula for the solution at late times is also obtained

properties of some weighted sobolev spaces and application to spectral approximations the weighted sobolev spaces on a square whose weight is a given power of the product of the distances to the edges are introduced trace theorems related to these spaces are proved then a regularity result for the dirichlet problem for the laplace operator is proved next several projection operators with polynomial values are considered for which approximation results in weighted norms are stated finally a collocation spectral method for the dirichlet problem for the laplace operator with inhomogeneous boundary conditions is analyzed this work includes new results on chebyshev approximation

implicit runge kutta nystrom methods for general second order volterra integro differential equations abstract in this paper we derive m stage runge kutta nystrom methods for the numerical solution of general second order volterra integro differential equations these implicit methods are based on collocation techniques in certain polynomial spline spaces the question concerning the attainable order of convergence of such one step methods is completely answered

moments propagation for weak solutions of the vlasov poisson system in the three dimensional torus abstract we consider weak solutions to the three dimensional vlasov poisson system in the periodic case we show that the velocity moments of order 3 can be propagated

propagation of moments and regularity for the 3 dimensional vlasov poisson system we prove that if the initial data has moments inv higher than three then the solution of vlasov poisson has also moments inv higher than three we deduce from this different regularity results on the local density the force field or the solution itself also we give a new uniqueness result and new regularity results for solutions satisfying only the energy andl bounds our proofs are based on a new representation formula and logarithmic estimates for the force field

spectral methods in time for a class of parabolic partial differential equations in this paper we introduce a fully spectral solution for the partial differential equation u t uu x vu x x mu x x x lu x x x x 0 for periodic boundary conditions in space the use of fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a chebyshev series boundary conditions other than periodic may still be treated with reasonable though lesser efficiency for all cases very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time

on the controllability of the vlasov poisson system in this paper we study the controllability of the vlasov poisson system in a periodic domain by means of an interior control located in an spatial subdomain the first result proves the local exact zero controllability in the two dimensional torus between two small acceptable distribution functions with an arbitrary control zone a second result establishes the global exact controllability in arbitrary dimension provided the control zone satisfies the condition that it contains a hyperplane of the torus

quintic b spline collocation method for fourth order partial integro differential equations with a weakly singular kernel quintic b spline collocation method for the numerical solution of fourth order partial integro differential equations is considered the scheme is based on the second order backward differential formula in the time direction and the quintic b spline method for the spatial derivative some numerical experiments are included to demonstrate the effectiveness of the discrete technique from the numerical experiments we can find that the present scheme possesses high accuracy and efficiency and the numerical results are in good agreement with the exact solutions

space time spectral element methods for one dimensional nonlinear advection diffusion problems abstract the following space time galerkin spectral element methods are developed and applied to solve the burgers equation with small viscosity a coupled methods consisting of an explicit method for hyperbolic dominated equations and an implicit method for parabolic dominated equations b two splitting methods which solve the hyperbolic substep explicitly and the parabolic one implicitly one uses spectral elements in the explicit part and the other uses the adams bashforth multistep method a subcycling technique in which several convective steps are taken for each implicit viscous step was also investigated for the two splitting methods a stability analysis of the four methods is performed and subsequent results are debated a convergence study and a comparison of computer execution time for the four methods is made and the results are discussed comparative study leads to the conclusion that the space time spectral element splitting method with subcycling is superior to the other methods presented in terms of robustness and computer execution time the number of subcycles should be kept low 2 3 in order to avoid significant loss of accuracy the coupled explicit method is also applied to the solution of the one dimensional coupled continuity momentum and energy equations for non isothermal flow of an ideal gas with temperature dependent properties in a cylindrical duct of variable radius

regularity of finite dimensional realizations for evolution equations we show that a continuous local semiflow of ck maps on a finite dimensional ck manifoldm can be embedded into a local ck flow on m under some weak necessary assumptions this result is applied to an open problem in 2 we prove that finite dimensional realizations for interest rate models are highly regular objects namely given by submanifolds m of d a where a is the generator of a strongly continuous semigroup

skew convolution semigroups and affine markov processes a general affine markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup we provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup the corresponding affine markov process is constructed as the strong solution of a system of stochastic equations with non lipschitz coefficients and poisson type integrals over some random sets based on this characterization it is proved that the affine process arises naturally in a limit theorem for the difference of a pair of reactant processes in a catalytic branching system with immigration

the semigeostrophic equations discretized in reference and dual variables we study the evolution of a system of n particles x i v i i 1 n in mathbb r 2d that system is a conservative system with a hamiltonian of the form h mu w 2 2 mu nu n where w2 is the wasserstein distance and is a discrete measure concentrated on the set x i v i i 1 n typically 0 is a discrete measure approximating an initial l density and can be chosen randomly when d 1 our results prove convergence of the discrete system to a variant of the semigeostrophic equations we obtain that the limiting densities are absolutely continuous with respect to the lebesgue measure when nu n n 1 infty converges to a measure concentrated on a special d dimensional set we obtain the vlasov monge ampere vma system when d 1 the vma system coincides with the standard vlasov poisson system

global weak solutions of the vlasov maxwell system with boundary conditions boundaries occur naturally in physucal systems which satisfy the vlasov maxwell system assume perfect conductor boundary conditions for maxwell and either specular reflection or partial absorption for vlasov then weak solutions with finite energy exist for all time

convergence of a semi lagrangian scheme for the one dimensional vlasov poisson system a semi lagrangian scheme is proposed for solving the periodic one dimensional vlasov poisson system in phase space on unstructured meshes the distribution function f t x v and the electric field e t x are shown to converge to the exact solution values in the l infty norm the rate of convergence is in o h4 3

discrete galerkin method for fredholm integro differential equations with weakly singular kernels approximations to a solution and its derivatives of a boundary value problem of an nth order linear fredholm integro differential equation with weakly singular or other nonsmooth kernels are determined these approximations are piecewise polynomial functions on special graded grids for their finding a discrete galerkin method and an integral equation reformulation of the boundary value problem are used optimal global convergence estimates are derived and an improvement of the convergence rate of the method for a special choice of parameters is obtained to illustrate the theoretical results a collection of numerical results of a test problem is presented

spectral methods in time for hyperbolic equations a pseudospectral numerical scheme for solving linear periodic hyperbolic problems is described it has infinite accuracy both in time and in space the high accuracy in time is achieved without increasing the computational work and memory space which is needed for a regular one step explicit scheme the algorithm is shown to be optimal in the sense that among all the explicit algorithms of a certain class it requires the least amount of work to achieve a certain given resolution the class of algorithms referred to consists of all explicit schemes which may be represented as a polynomial in the spatial operator

finite element methods for partial volterra integro differential equations on two dimensional unbounded spatial domains abstract the precise and effective way for solving a partial volterra integro differential equation on unbounded spatial domain is to derive artificial boundary conditions for some feasible and prescribed computational domain thus the unsolvable problem on unbounded domain is converted to the computational problem on bounded domain which is often called reduced problem a feasible numerical method will then be applied to solve the reduced problem with the artificial boundary conditions which often exhibit nonlocal properties in this paper the finite element method for the spatial space and the recently developed discontinuous galerkin time stepping method for the temporal space are considered to solve the reduced problem the convergence rate explicitly with those interesting parameters spatial grid size h temporal mesh size k the location of the artificial boundary d and the truncation number m is obtained this paper is the first theoretical analysis of the numerical methods for volterra integro differential equations on unbounded spatial domains

spectral methods in time for parabolic problems a pseudospectral explicit scheme for solving linear periodic parabolic problems is described it has infinite accuracy both in time and in space the high accuracy is achieved while the time resolution parameter m m o 1 delta t for time marching algorithm and the space resolution parameter n n o 1 delta x must satisfy m o n 1 varepsilon varepsilon 0 compared to the common stability condition m o n 2 which must be satisfied in any explicit finite order time algorithm

weak turbulence plasma induced by two scale homogenization abstract this paper is devoted to the homogenization of the quasilinear theory of the plasma turbulence described by the vlasov poisson system it is shown that the homogenization limit in the sense of two scale limit of the distribution function satisfies the linear vlasov poisson equations moreover the limit distribution function can be decomposed into the mean and the fluctuation parts and the mean part the equilibrium distribution function is shown to be the solution of the nonlocal quasilinear velocity space diffusion equation we also investigate the landau damping from the point of view of homogenization through the two scale limit

unstable and stable galaxy models to determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the vlasov theory for galaxy dynamics in this article we study the stability of isotropic spherical symmetric galaxy models f0 e for which the distribution function f0 depends on the particle energy e only in the first part of the article we derive the first sufficient criterion for linear instability of f0 e f0 e is linearly unstable if the second order operator a 0 equiv delta 4 pi int f 0 prime e i mathcal p dv has a negative direction where mathcal p is the projection onto the function space g e l l being the angular momentum see the explicit formulae 29 and 28 in the second part of the article we prove that for the important king model the corresponding a0 is positive definite such a positivity leads to the nonlinear stability of the king model under all spherically symmetric perturbations

numerical solution of parabolic integro differential equations by the discontinuous galerkin method the numerical solution of a parabolic equation with memory is considered the equation is first discretized in time by means of the discontinuous galerkin method with piecewise constant or piecewise linear approximating functions the analysis presented allows variable time steps which as will be shown call then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data the combination with finite element discretizat in space is also studied

on a class of quasilinear partial integrodifferential equations with singular kernels abstract we prove local and global existence theorems for a model equation in nonlinear viscoelasticity in contrast to previous studies we allow the memory function to have a singularity we approximate the equation by equations with regular kernels and use energy estimates to prove convergence of the approximate solutions

on the lagrangian structure of transport equations the vlasov poisson system the vlasov poisson system is an important nonlinear transport equation used to describe the evolution of particles under their self consistent electric or gravitational field the existence of classical solutions is limited to dimensions d 3 under strong assumptions on the initial data whereas weak solutions are known to exist under milder conditions however in the setting of weak solutions it is unclear whether the eulerian description provided by the equation physically corresponds to a lagrangian evolution of the particles in this article we develop several general tools concerning the lagrangian structure of transport equations with nonsmooth vector fields and we apply these results to show that weak renormalized solutions of vlasov poisson are lagrangian and actually that the concepts of renormalized and lagrangian solutions are equivalent as a corollary we prove that finite energy solutions in dimension d 4 are transported by a global flow in particular they preserve all the natural casimir invariants and we obtain the global existence of weak solutions in any dimension under minimal assumptions on the initial data

crank nicolson and legendre spectral collocation methods for a partial integro differential equation with a singular kernel abstract in this paper we present an efficient numerical method for the solution of a partial integro differential equation with a singular kernel in the time direction a crank nicolson finite difference scheme is used to approximate the differential term and the product trapezoidal method is employed to treat the integral term also for space discretization we apply legendre spectral collocation method we discuss the stability and convergence of proposed method and show that the method is unconditionally stable and convergent with order o 3 2 n s where n and s are time step size number of collocation points and regularity of exact solution respectively we compare the numerical results of proposed method with the results of other schemes in the literature in terms of accuracy computational order and cpu time to show the efficiency and applicability of it

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

the vlasov equation with infinite mass we show existence and uniqueness for the solutions to the vlasov equation for a positive smooth and short range potential in the case of unbounded mass

crank nicolson quasi wavelets method for solving fourth order partial integro differential equation with a weakly singular kernel in this paper we study a novel numerical scheme for the fourth order partial integro differential equation with a weakly singular kernel in the time direction a crank nicolson time stepping is used to approximate the differential term and the product trapezoidal method is employed to treat the integral term and the quasi wavelets numerical method for space discretization our interest in the present paper is a continuation of the investigation in yang et al 33 where we study discretization in time by using the forward euler scheme the comparisons of present results with the previous ones show that the present scheme is more stable and efficient for numerically solving the fourth order partial integro differential equation with a weakly singular kernel we also tested the method proposed on several one and two dimensional problems with very promising results besides in order to demonstrate the power of the quasi wavelets method in comparison with standard discretization methods we also consider the high frequency oscillation problems with the integro differential term

linear stability of the vlasov poisson system with boundary conditions abstract we study the linear stability of the vlasov poisson system in one dimension on a finite interval and half line with the in flow and specular reflection boundary conditions conditions for the existence and non existence of stationary solutions are obtained the behavior of the perturbed solutions is investigated in different contexts we show that if the equilibrium distribution is a strictly decreasing function of local energy density then the vlasov poisson system on a finite interval is stable in the weighted l 2 sense for the in flow and specular reflection boundary conditions for the case is strictly increasing we prove a similar result on a finite interval under some extra assumptions finally in the last part of the article the spectral stability of the vlasov poisson system on an unbounded interval is studied with similar monotonicity assumptions on

on the 3 d vlasov poisson system with point charges global solutions with unbounded supports and propagation of velocity spatial moments abstract a new energy functional which is shown to decay to zero as time tends to infinite is introduced for the three dimensional vlasov poisson plasma in the presence of heavy point charges with repulsive interaction moreover a new kind of pointwise energy of a plasma particle relative to each point charge is also constructed and the variation of its root is shown to be controlled by the electrostatic fields based on those results we prove global existence and uniqueness of a classical solution possibly having infinite kinetic energy but with compact velocity spatial support specified in theorem 1 1 furthermore for the single point charge vlasov poisson plasma global existence and polynomial propagation of velocity spatial moments of weak solutions are also established

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

on the controllability of the vlasov poisson system in the presence of external force fields in this work we are interested in the controllability of vlasov poisson systems in the presence of an external force field namely a bounded force field or a magnetic field by means of a local interior control we are able to extend the results of 7 where the only present force was the self consistent electric field

space time spectral method for a weakly singular parabolic partial integro differential equation on irregular domains abstract the spectral method is proposed for the partial integro differential equations with a weakly singular kernel on irregular domains the space discretization is based on the nodal spectral element method using the lagrange polynomials basis associated with the gauss lobatto legendre quadrature nodes also the model is discretized in time with the legendre spectral galerkin method the discretization leads to conversion of the problem to a sylvester matrix equation which can be solved efficiently by the qz algorithm gardiner et al 1992 the convergence of the method is proven by providing a priori l 2 error estimate numerical results illustrate the efficiency and spectral accuracy of the proposed method

the vlasov poisson system with infinite kinetic energy and initial data in lp r6 abstract in this paper the global existence of weak solutions to the three dimensional vlasov poisson system with infinite kinetic energy and initial data in l p r 6 is studied the propagation of low moments in the velocity variables is also proved

finite element methods for parabolic and hyperbolic partial integro differential equations on formule plusieurs methodes de galerkin a temps discret pour des equations integrodifferentielles paraboliques

on spectral methods for volterra type integro differential equations this paper considers the spectral methods for a volterra type integro differential equation firstly the volterra type integro differential equation is equivalently restated as two integral equations of the second kind secondly a legendre collocation method is used to solve them then the error analysis is conducted based on the l norm in addition numerical results are presented to confirm our analysis

piecewise polynomial collocation methods for linear volterra integro differential equations with weakly singular kernels in the first part of this paper we study the regularity properties of solutions of linear volterra integro differential equations with weakly singular or other nonsmooth kernels we then use these results in the analysis of two piecewise polynomial collocation methods for solving such equations numerically the main purpose of the paper is the derivation of optimal global convergence estimates and the analysis of the attainable order of local superconvergence at the collocation points

bernstein series solutions of multidimensional linear and nonlinear volterra integral equations with fractional order weakly singular kernels abstract this paper proposes a quadrature method based on multi variate bernstein polynomials the method is used to solve multidimensional volterra integral equations with weakly singular kernels firstly we use multi variate bernstein polynomials to approximate the unknown function of an equation then a discrete function equation can be obtained by substituting the approximate solution into the equation secondly the discrete function system is transformed into an algebra equation system by using some discrete points we can perform the integral operations without discrete kernel function and the weakly singular integrals can be calculated directly by using quadrature method so the method is easy to implement thirdly we prove the existence and uniqueness of the solution of the approximate equation as well as the error analysis of the proposed method six numerical examples are given to illustrate the efficiency of this method

existence of limiting distribution for affine processes abstract in this paper sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space r 0 m r n where m n z 0 with m n 0 our main theorem extends and unifies some known results for ou type processes on r n and one dimensional cbi processes with state space r 0 to prove our result we combine analytical and probabilistic techniques in particular the stability theory for odes plays an important role

time asymptotics for solutions of vlasov poisson equation in a circle we prove that there exists a class of solutions of the nonlinear vlasov poisson equation vpe on a circle that converges weakly as t to a stationary homogeneous solution of vpe this behavior is called in the linear case landau damping the result is obtained by constructing a suitable scattering problem for the solutions of the vlasov poisson problem a consequence of this result is that a class of stationary solutions of the vlasov poisson equation is unstable in a weak topology

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

solving parabolic integro differential equations by an explicit integration method vasudeva murthy a s and j g verwer solving parabolic integro differential equations by an explicit integration method journal of computational and applied mathematics 39 1992 121 132 the subject of this note is the numerical integration in time of nonclassical parabolic initial boundary value problems which involve nonlocal integral terms over the spatial domain the integral terms may appear in the boundary conditions and or in the governing partial differential equation itself these terms generally complicate the application of standard methods our purpose here is to draw attention to an explicit method the runge kutta chebyshev method whose application remains straightforward in many cases of practical interest we discuss two numerical examples to illustrate this a comparison is made respectively with the implicit bdf code dassl and with the keller box scheme

time evolution of an infinitely extended vlasov system with singular mutual interaction we study the time evolution of an infinitely extended system in the mean field approximation governed by the vlasov equation this system is confined in an unbounded cylinder by an external force singular on the border the mutual interaction is assumed singular at short distance as 1 r alpha with alpha 2 3 or alpha 1 in case of an external lorentz force and with a short range the initial density is assumed bounded differently from studies which assume initial data compact in space and or in velocities here we consider a system having infinite mass and an exponential bound on the velocities according to the maxwell boltzmann law

bounds on the growth of the velocity support for the solutions of the vlasov poisson equation in a torus a bound on the growth of the velocity for the vlasov poisson equation in a torus is given in one and two dimensions the main tool used in the proof is a partition into fast and slow particles and the ergodic property of the free motion in a torus

chebyshev spectral solution of nonlinear volterra hammerstein integral equations abstract in this paper the chebyshev spectral cs method for the approximate solution of nonlinear volterra hammerstein integral equations f o k r g r y r d r 0 t is investigated the method is applied to approximate the solution not to the equation in its original form but rather to an equivalent equation z t g t y t t 1 1 the function z is approximated by the nth degree interpolating polynomial zn with coefficients determined by discretizing g t y t at the chebyshev gauss labatto nodes we then define the approximation to y to be of the form y n t f t 1 1 k t s z n s d s 1 1 and establish that under suitable conditions limn yn t y t uniformly in t finally a numerical experiment for a nonlinear volterra hammerstein integral equation is presented which confirms the convergence demonstrates the applicability and the accuracy of the chebyshev spectral cs method

on global existence for the vlasov poisson system in a half space abstract we prove global existence for the vlasov poisson system in a half space in the plasma physics case assuming homogeneous dirichlet boundary conditions for the electric potential our proof uses an adaptation of pfaffelmoser s method and it provides also a different proof of the previously known global existence results for the vlasov poisson system in a half space with neumann boundary conditions for the electric potential we also obtain a large class of one dimensional stationary solutions for the problem with neumann boundary conditions

non equilibrium dynamics of three dimensional infinite particle systems we show existence and uniqueness for the solutions to the newton equations relative to a system of infinitely many particles in the space interacting by means of a positive and short range potential the initial conditions are chosen in a set sufficiently large to be the support of any reasonable non equilibrium state we extend previous results in one and two dimensions obtained by lanford and by fritz and dobrushin respectively many years ago

the lagrange galerkin spectral element method on unstructured quadrilateral grids the purpose of this paper is to introduce a new method formed by fusing the lagrange galerkin and spectral element methods the lagrange galerkin method traces the characteristic curves of the solution and consequently is very well suited for resolving the nonlinearities introduced by the advection operator of the fluid dynamics equations spectral element methods are essentially higher order finite element methods that exhibit spectral exponential convergence provided that the solution is a smooth function by combining these two methods a numerical scheme can be constructed that resolves with extremely high precision the nonlinearities of the advection terms and the smooth regions of the flow generated by the diffusion terms this paper describes the construction of the lagrange galerkin spectral element method which permits the use of any grid type including unstructured grids the only restriction at the moment is that the grid elements be quadrilaterals the stability analysis of both methods demonstrates why these two methods are so powerful individually and how their fusion leads to an improved scheme the lagrange galerkin spectral element method is validated using the 1d and 2d advection and advection diffusion equations the results of the stability analysis and the numerical experiments demonstrate the utility of such an approach

error estimates for semidiscrete finite element methods for parabolic integro differential equations application des methodes d elements finis aux equations integro differentielles de type parabolique avec un noyau integral forme par un operateur aux derivees partielles d ordre 2

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

quasineutral limit for vlasov poisson via wasserstein stability estimates in higher dimension abstract this work is concerned with the quasineutral limit of the vlasov poisson system in two and three dimensions we justify the formal limit for very small but rough perturbations of analytic initial data generalizing the results of 12 to higher dimension

mechanisms of lagrangian analyticity in fluids certain systems of inviscid fluid dynamics have the property that for solutions that are only slightly better than differentiable in eulerian variables the corresponding lagrangian trajectories are analytic in time we elucidate the mechanisms in fluid dynamics systems that give rise to this automatic lagrangian analyticity as well as mechanisms in some particular fluids systems which prevent it from occurring we give a conceptual argument for a general fluids model which shows that the fulfillment of a basic set of criteria results in the analyticity of the trajectory maps in time we then apply this to the incompressible euler equations to prove analyticity of trajectories for vortex patch solutions we also use the method to prove that the lagrangian trajectories are analytic for solutions to the pressureless euler poisson equations for initial data with moderate regularity we then examine the compressible euler equations and find that the finite speed of propagation in the system is incompatible with the lagrangian analyticity property by taking advantage of this finite speed we construct smooth initial data with the property that some corresponding lagrangian trajectory is not analytic in time we also study the vlasov poisson system uncovering another mechanism that deters the analyticity of trajectories in this case a key nonlocal operator does not preserve analytic dependence in time for this system we also construct smooth initial data for which the corresponding solution has some non analytic lagrangian trajectory providing a counterexample to lagrangian analyticity for a system in which there is an infinite speed of propagation

orbital stability of spherical galactic models we consider the three dimensional gravitational vlasov poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters a well known conjecture is the stability of spherical models which are nonincreasing radially symmetric steady states solutions this conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by antonov in 1961 in a previous work we derived the stability of anisotropic models under it spherically symmetric perturbations using fundamental monotonicity properties of the hamiltonian under suitable generalized symmetric rearrangements first observed in the physics litterature in this work we show how this approach combined with a it new generalized antonov type coercivity property implies the orbital stability of spherical models under general perturbations

finite speed propagation of the solutions for the relativistic vlasov maxwell system in this paper we investigate the continuous dependence with respect to the initial data of the solutions for the 1d and 1 5d relativistic vlasov maxwell system more precisely we prove that these solutions propagate with finite speed we formulate our results in the framework of mild solutions i e the particle densities are solutions by characteristics and the electro magnetic fields are lipschitz continuous functions

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

affine processes are regular we show that stochastically continuous time homogeneous affine processes on the canonical state space mathbb r geq 0 m times mathbb r n are always regular in the paper of duffie et al ann appl probab 13 3 984 1053 2003 regularity was used as a crucial basic assumption it was left open whether this regularity condition is automatically satisfied for stochastically continuous affine processes we now show that the regularity assumption is indeed superfluous since regularity follows from stochastic continuity and the exponentially affine form of the characteristic function for the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of spdes

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

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

quasi wavelet based numerical method for a class of partial integro differential equation abstract in this paper we study the numerical solution of initial boundary problem for a class of partial integro differential equations the quasi wavelet method is proposed to handle the spatial derivatives while the forward euler method is used to discretize the temporal derivatives detailed discrete schemes are given and some numerical experiments are included to demonstrate the effectiveness of the discrete technique the comparisons of the present numerical results with the exact analytical solutions show that the quasi wavelet based numerical method has distinctive local property and can achieve accurate results

finite element approximation of a parabolic integro differential equation with a weakly singular kernel we give error estimates for the numerical solution by means of the galerkin finite element method of an integro differential equation of parabolic type with a memory term containing a weakly singular kernel optimal order estimates are shown for spatially semidiscrete and completely discrete methods special attention is paid to the regularity of the exact solution

the screened poisson vlasov system with infinite charge and vanishing screening the vlasov equation may be used to model the dynamics of a collisionless plasma we consider a situation where the plasma has unbounded support and the charge density does not decay as x the electric field is computed from the screened poisson equation whose fundamental solution decays exponentially as x and hence gives a convergent integral despite the lack of decay of the charge density the limit as the screening is removed is studied in one space dimension it is shown that if some assumptions on the initial conditions hold then the limit in question exists but is not uniform and the problem satisfied by the limit is identified

the cauchy problem for the 3 d vlasov poisson system with point charges in this paper we establish global existence and uniqueness of the solution to the three dimensional vlasov poisson system in the presence of point charges with repulsive interaction the present analysis extends an analogous two dimensional result caprino and marchioro in kinet relat models 3 2 241 254 2010

the spectral methods for parabolic volterra integro differential equations in this paper we study the numerical solutions to parabolic volterra integro differential equations in one dimensional bounded and unbounded spatial domains in a bounded domain the given parabolic volterra integro differential equation is converted to two equivalent equations then a legendre collocation method is used to solve them and finally a linear algebraic system is obtained for an unbounded case we use the algebraic mapping to transfer the problem on a bounded domain and then apply the same presented approach for the bounded domain in both cases some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method

space time spectral element method for solution of second order hyperbolic equations abstract a two field mixed hybrid spectral element formulation in time and space is presented explicit stsee and implicit stsei algorithms are developed and used to solve a second order scalar hyperbolic equation the algorithms were analyzed and their characteristics in terms of truncation error and stability are presented this analysis was confirmed by numerical results the improvement in accuracy in comparison with semi discrete schemes is remarkable

global existence for the vlasov poisson system in bounded domains in this paper we prove global existence for solutions of the vlasov poisson system in convex bounded domains with specular boundary conditions and with a prescribed outward electrical field at the boundary

a uniqueness criterion for unbounded solutions to the vlasov poisson system we prove uniqueness for the vlasov poisson system in two and three dimensions under the condition that the l p norms of the macroscopic density grow at most linearly with respect to p this allows for solutions with logarithmic singularities we provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow up in the gravitational two dimensional case such states are intimately related to radially symmetric steady solutions of the system our method relies on the lagrangian formulation for the solutions exploiting the second order structure of the corresponding ode