branching rules for the supergroup su n m from those of su n m the decomposition of representations of supergroups into representations of subgroups is needed in practical applications in this paper we set up and exploit a fruitful one to one correspondence between the lie group branching su n m su n su m u 1 and the supergroup branchings su n m su n su m u 1 and su n1 n2 m1 m2 su n1 m1 su n2 m2 u 1 a simple and useful prescription is discovered for obtaining the su n m branching rules from those of su n m for any representation a large class of examples sufficient for many physical applications we can foresee are explicitly worked out and tabulated

the generalized atypical supertableaux of the orthosymplectic groups osp 2 2p the classification and the interpretation of the young supertableaux of the orthosymplectic group osp 2 2p are given a particular emphasis is made on the generalized atypical supertableaux associated to nonfully reducible atypical representations

global strong solutions of two dimensional navier stokes equations with nonlinear slip boundary conditions abstract the two dimensional time dependent navier stokes equations with nonlinear slip boundary conditions are investigated in this paper since the nonlinear slip boundary conditions of this type include the subdifferential property the weak variational formulation is the variational inequality the existence uniqueness and regularity of global weak solutions are shown using the regularized method moreover the continuous dependence property of the weak solution for given initial data and the behavior of the global weak solution as t are established

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

mixed boundary value problems for the stationary navier stokes system in polyhedral domains the authors consider boundary value problems for the navier stokes system in a polyhedral domain where different boundary conditions in particular dirichlet neumann slip conditions are arbitrarily combined on the faces of the polyhedron they prove existence and regularity theorems for weak solutions in weighted and nonweighted l p sobolev and holder spaces with sharp integrability and smoothness parameters

the existence of solitary wave solutions of delayed camassa holm equation via a geometric approach abstract this paper is concerned with the camassa holm equation which is a model for shallow water waves we first establish the existence of solitary wave solutions for the equation without delay and then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system especially the geometric singular perturbation theory and invariant manifold theory according to the relationship between solitary wave and homoclinic orbit the camassa holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution it is proved that the equation with disturbance also possesses homoclinic orbit and there exists solitary wave solution of the delayed camassa holm equation

spatiotemporal dynamics of continuum neural fields we survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields neural fields model the large scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial distribution of neuronal synaptic connections they provide an important example of spatially extended excitable systems with nonlocal interactions and exhibit a wide range of spatially coherent dynamics including traveling waves oscillations and turing like patterns

existence and uniqueness of travelling waves for a neural network a one dimensional scalar neural network with two stable steady states is analysed it is shown that there exists a unique monotone travelling wave front which joins the two stable states some additional properties of the wave such as the direction of its velocity are discussed

for the vorticity velocity pressure form of the navier stokes equations on a bounded plane domain with corners abstract we show existence and regularity for the boundary value problems of the navier stokes equations with non standard bcs on a bounded plane domain with non convex corners we assign the vorticity value 0 and the velocity normal component u n u 0 n over the non convex corner the dynamic pressure value p u 2 2 p 0 over inflow and outflow boundaries and so on we construct the corner singularity functions for the stokes operator with zero vorticity and velocity normal component bcs subtract its leading singularity from the solution by defining the coefficient of the singularity and show increased regularity for the remainder the solution is determined by the smoother part and the coefficients of the singularities it is seen from the singularity that the dynamic pressure has a transition layer that changes the sign at 2 in the domain the obtained results can be applied to general polygonal domains and the cavity flows

branching rules for a class of typical and atypical representations of gl m n the irreducible representations of the lie superalgebra gl m n with highest weights of the form 1 2 m are investigated using a recently introduced induced module construction for atypical modules the gl m n gl m n 1 branching rules are obtained and a suitable gel fand tsetlin basis is introduced the class of representations considered includes some multiply atypical irreducible representations of gl m n and all irreducible representations of gl m 1

composite young diagrams supercharacters of u m n and modification rules the supercharacter of u m n associated with an arbitrary composite young diagram is defined the distinction is made between standard and non standard supercharacters a modification rule is presented which may be used to express any non standard supercharacter in terms of standard supercharacters in the case n 0 the rule reduces to the rule already known to be appropriate to u m

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

spectral discretization of the axisymmetric vorticity velocity and pressure formulation of the navier stokes problem we deal in this work with the nonlinear navier stokes equations set in a three dimensional axisymmetric bounded domain the boundary conditions that we consider are given on the normal component of the velocity and the tangential component of the vorticity such conditions occur in a large number of flows and we are led to write a vorticity velocity pressure formulation under assumptions on the data of the problem the three dimensional problem is reduced in a two dimensional one for the discretization we use the spectral methods which are well adapted here we prove the well posedness of the obtained formulations and we derive optimal error estimates on the three unknowns the results of the numerical experiments for known functions and a given data corresponding to a poiseuille type flow are coherent with the theoretical ones

numerical methods for the stokes and navier stokes equations driven by threshold slip boundary conditions abstract in this article we discuss the numerical solution of the stokes and navier stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions to solve the stokes system we first reduce the related variational inequality into a saddle point point problem for a well chosen augmented lagrangian to solve this saddle point problem we suggest an alternating direction method of multiplier together with finite element approximations the solution of the navier stokes system combines finite element approximations time discretization by operator splitting and augmented lagrangian method numerical experiment results for two and three dimensional flow confirm the interest of these approaches

spectral discretization of the vorticity velocity and pressure formulation of the navier stokes equations we consider the navier stokes equations in a two or three dimensional domain provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity we write a variational formulation of this problem with three independent unknowns the vorticity the velocity and the pressure and prove the existence of a solution for this problem next we propose a discretization by spectral methods which relies on this formulation in the two dimensional case we prove quasi optimal error estimates for the three unknowns we conclude with some numerical experiments nous considerons les equations de navier stokes dans un domaine biou tri dimensionnel munies de conditions aux limites non usuelles portant sur la composante normale de la vitesse et la ou les composantes tangentielles du tourbillon nous ecrivons une formulation variationnelle de ce probleme qui comporte trois inconnues independantes le tourbillon la vitesse et la pression nous prouvons que ce probleme admet au moins une solution nous proposons une discretisation par methodes spectrales construite a partir de cette formulation dans le cas bidimensionnel nous etablissons des majorations quasi optimales de l erreur pour les trois inconnues nous concluons par quelques experiences numeriques

branching rules for typical and atypical representations of gl n 1 the gl n 1 down arrow gl n gl 1 branching rules are determined for all finite dimensional irreducible typical and atypical representations of gl n mod 1 using a recently introduced induced module construction for atypical modules and confirm those found recently by palev 1988 by another method the lowest weights and characters of the irreducible representations are found and the validity for gl n mod 1 of the character formula conjectured by hughes and king 1987 is confirmed some generalisations and extensions of the method are discussed

mixed supertableaux of the superunitary groups ii su n m the young supertableaux of the superunitary groups are studied we give the conditions on the size of legal supertableaux the type of atypicity for tensor representations which are irreducible making the link between the kac dynkin parameters and those of the supertableau a discussion is given on nonfully reducible representations and generalized atypical supertableaux

center manifolds without a phase space we establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line the class of equations includes most importantly nonlinear equations with nonlocal coupling through convolution operators as they arise in the description of spatially extended dynamics in neuroscience these systems possess a natural spatial translation symmetry but local existence or uniqueness theorems for a spatial evolution associated with this spatial shift or even a well motivated choice of phase space for the induced dynamics do not seem to be available due to the infinite range forward and backward coupling through nonlocal convolution operators we perform a reduction relying entirely on functional analytic methods despite the nonlocal nature of the problem we do recover a local differential equation describing the dynamics on the set of small bounded solutions exploiting that the translation invariance of the original problem induces a flow action on the center manifold we apply our reduction procedure to problems in mathematical neuroscience illustrating in particular the new type of algebra necessary for the computation of taylor jets of reduced vector fields

generating functions and elementary young tableaux when constructing polynomial bases for group representations one is led naturally to consider a stretched product of states elementary multiplets are states that cannot be expressed as the stretched product of any other two states and they can be identified with terms occurring in certain generating functions in this paper the authors define an analogous stretched product of young tableaux together with elementary tableaux these may be used in a manner similar to elementary multiplets to construct generating functions they consider several examples where this method can be applied and in particular give new large n rank free branching rule generating functions for the group subgroup pairs su n su m contained in implied by su n m first four labels non zero so n contained in implied by su n first three labels non zero and sp 2n contained in implied by su 2n first five labels non zero this method of finding these generating functions uses the theory of grobner bases which allows the authors to make precise the notion of compatibility relations or forbidden products of elementary tableaux

young diagrams supercharacters of osp m n and modification rules the supercharacter of osp m n associated with an arbitrary young diagram is defined the distinction is made between osp m n standard and non standard supercharacters the corresponding modification rule which may be used to express a non standard supercharacter in terms of standard supercharacters is presented exemplified and proved this rule involves the removal of n 2 1 boundary strips from the young diagram in the case n 0 the rule reduces to the well known rule appropriate to o m for a non standard supercharacter corresponding to a typical irreducible representation of osp m n the modification yields a single typical standard supercharacter on the other hand for a non standard supercharacter corresponding to an atypical irreducible representation the rule yields a linear combination of atypical standard supercharacters

representations of supergroups an explicit construction of representations of supergroups is given in terms of direct products of covariant and contravariant fundamental representations the rules of supersymmetrization are characterized by extended young supertableaux this constructive approach leads to explicit transformation properties of higher representations as well as to closed explicit formulas for characters from which other invariants such as dimensions and eigenvalues of all casimir operators can be calculated we have applied this approach so far to the supergroups su n m osp n 2m p n for which we have obtained all the representations constructible as direct products of the fundamental defining representations an argument is presented toward the irreducibility of all these representations

anomalies and eigenvalues of casimir operators for lie groups and supergroups an expression for the anomaly of any representation of the su n groups and su n m supergroups is presented some anomaly free complex representations of su n and su n m are pointed out for su n these occur for n 5 and for large dimensions for su n m they already occur for low dimensions also a generating function to obtain the eigenvalues of all casimir operators of su n m is given and an extension to other supergroups is pointed out

variational inequality for the rotating navier stokes equations with subdifferential boundary conditions a steady viscous incompressible fluid through a rotating channel satisfies the rotating navier stokes equations subdifferential boundary conditions are imposed a variational inequality is derived for this system furthermore under some assumptions the weak solution of the variational inequality exists and is unique

korn s inequalities and their applications in continuum mechanics korn s inequalities have played a central role in the development of linear elasticity not only in connection with the basic theoretical issues such as existence and uniqueness but also in a variety of applications the korn inequalities and other related inequalities for integrals of quadratic functionals also arise in the analysis of viscous incompressible fluid flow the dimensionless optimal constants appearing in these inequalities the korn constants depend only on the shape of the domains of concern information on the geometric dependence of these constants is essential in applications in this review article we summarize the major results on korn s inequalities for bounded domains in two and three dimensions with emphasis on results concerning the korn constants some applications in continuum mechanics are also described

finite dimensional representations of the lie superalgebra sl 1 3 in a gel fand zetlin basis ii nontypical representations in a series of two papers all finite dimensional irreducible representations of the special linear lie superalgebra sl 1 3 are constructed explicit formulas for the generators in an orthonormal gel fand zetlin basis of the even subalgebra gl 3 are given this paper develops a background for constructing the representations expressions for the transformation properties of the basis under the action of the generators are written down within all typical sl 1 3 modules

stokes system with local coulomb s slip boundary conditions analysis of discretized models and implementation abstract the theoretical part of the paper analyzes discretized stokes systems with local coulomb s slip boundary conditions solutions to discrete models are defined by means of fixed points of an appropriate mapping we prove the existence of a fixed point establish conditions guaranteeing its uniqueness and examine how they depend on the discretization parameter h and the slip coefficient the second part of the paper is devoted to computational aspects numerical experiments are presented

fast and slow waves in the fitzhugh nagumo equation abstract it is known that the fitzhugh nagumo equation possesses fast and slow travelling waves fast waves are perturbations of singular orbits consisting of two pieces of slow manifolds and connections between them whereas slow waves are perturbations of homoclinic orbits of the unperturbed system we unfold a degenerate point where the two types of singular orbits coalesce forming a heteroclinic orbit of the unperturbed system let c denote the wave speed and e the singular perturbation parameter we show that there exists a c 2 smooth curve of homoclinic orbits of the form c e c connecting the fast wave branch to the slow wave branch additionally we show that this curve has a unique non degenerate maximum our analysis is based on a shilnikov coordinates result extending the exchange lemma of jones and kopell we also prove the existence of inclination flip points for the travelling wave equation thus providing the evidence of the existence of n homoclinic orbits n pulses for the fitzhugh nagumo equation for arbitrary n

vorticity velocity pressure formulation for stokes problem we propose a three field formulation for efficiently solving a twodimensional stokes problem in the case of nonstandard boundary conditions more specifically we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary the proposed computational methodology consists in reformulating the considered boundary value problem via a mixed type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the lagrange multiplier the obtained formulation is then discretized and a convergence analysis is performed a priori error estimates are established and some numerical results are presented to highlight the perfomance of the proposed computational methodology

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

an augmented mixed finite element method for the vorticity velocity pressure formulation of the stokes equations this paper deals with the numerical approximation of the stationary two dimensional stokes equations formulated in terms of vorticity velocity and pressure with non standard boundary conditions here by introducing a galerkin least squares term we end up with a stabilized variational formulation that can be recast as a twofold saddle point problem we propose two families of mixed finite elements to solve the discrete problem in the first family the unknowns are approximated by piecewise continuous and quadratic elements brezzi douglas marini and piecewise constant finite elements respectively while in the second family the unknowns are approximated by piecewise linear and continuous raviart thomas and piecewise constant finite elements respectively the wellposedness of the resulting continuous and discrete variational problems are studied employing an extension of the babuska brezzi theory we establish a priori error estimates in the natural norms and we finally report some numerical experiments illustrating the behavior of the proposed schemes and confirming our theoretical findings on structured and unstructured meshes additional examples of cases not covered by our theory are also presented

boundary layer analysis of the navier stokes equations with generalized navier boundary conditions we study the weak boundary layer phenomenon of the navier stokes equations with generalized navier friction boundary conditions u n 0 s u n tan au 0 in a bounded domain in r3 when the viscosity e 0 is small here s u is the symmetric gradient of the velocity u and a is a type 1 1 tensor on the boundary when a i we obtain navier boundary conditions and when a is the shape operator we obtain the conditions u n curlu n 0 by constructing an explicit corrector we prove the convergence as e tends to zero of the navier stokes solutions to the euler solution both in the natural energy norm and uniformly in time and space

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

stabilized finite element method for navier stokes equations with physical boundary conditions this paper deals with the numerical approximation of the 2d and 3d navier stokes equations satisfying nonstandard boundary conditions this lays on the finite element discretisation of the corresponding stokes problem which is achieved through a three fields stabilized mixed formulation a priori and a posteriori error bounds are established for the nonlinear problem ascertaining the convergence of the method finally numerical tests are presented including mesh refinement via error indicators

penalty finite element method for stokes problem with nonlinear slip boundary conditions abstract the penalty finite element method for stokes problem with nonlinear slip boundary conditions based on the finite element subspace v h m h which satisfies the discrete inf sup condition is investigated in this paper since this class of nonlinear slip boundary conditions include the subdifferential property the weak variational formulation associated with stokes problem is variational inequality under some regularity assumptions we obtain the optimal h 1 and l 2 error estimates between u and u h and between u and u h e where the error orders are e h for h 1 error and e h 2 for l 2 error

an integrodifferential model for phase transitions stationary solutions in higher space dimensions we study the existence and stability of stationary solutions of an integrodifferential model for phase transitions which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity as such this model is a nonlocal extension of the allencahn equation which incorporates long range interactions we find that the set of stationary solutions for this model is much larger than that of the allencahn equation

modification rules for orthosymplectic superalgebras modification rules are presented for finite dimensional graded tensor representations of osp m n with the representations specified by young supertableaux these rules relate non standard supertableaux to standard supertableaux via the removal of continuous boundary hooks all typical tensor representations are treated together with atypical representations which satisfy up to two atypically conditions

finite dimensional approximation of nonlinear problems part ii limit points note univ paris 6 f 75230 paris 05 france ecole polytech ctr math appl cnrs equipe rech 747 f 91128 palaiseau france univ pavia cnr ist anal numer i 27100 pavia italy brezzi f univ pavia cnr ist math appl i 27100 pavia italy isi document delivery no lr761times cited 54cited reference count 13 reference asn article 1981 002doi 10 1007 bf01396184 record created on 2006 08 24 modified on 2017 05 12

invariant manifolds in singular perturbation problems for ordinary differential equations based on fenichel s geometric idea invariant manifold theory is applied to singular perturbation problems this approach clarifies the nature of outer and inner solutions a specific condition is given to ensure the existence of heteroclinic connections between normally hyperbolic invariant manifolds a method to approximate the connections is also presented

spectral discretization of the vorticity velocity and pressure formulation of the stokes problem we consider the stokes problem in a square or a cube provided with nonstandard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity we write a variational formulation of this problem with three independent unknowns the vorticity the velocity and the pressure next we propose a discretization by spectral methods which relies on this formulation and since it leads to an inf sup condition on the pressure in a natural way we prove optimal error estimates for the three unknowns we present numerical experiments which are in perfect coherence with the analysis

two level variational multiscale finite element methods for navier stokes type variational inequality problem in this paper we present two level variational multiscale finite element method based on two local gauss integrations for navier stokes equations with friction boundary conditions which are of the form of navier stokes type variational inequality of the second kind we solve navier stokes type variational inequality problem on the coarse mesh and solve linearized navier stokes type variational inequality problem corresponding to newton iteration on the fine mesh the error estimates in h 1 norm for velocity and l 2 norm for pressure are derived meanwhile uzawa iteration schemes are constructed to solve the subproblems in this two level method finally the numerical results are displayed to support the theoretical analysis

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

local exact controllability of the navier stokes equations with the condition on the pressure on parts of the boundary in this paper we prove a local exact controllability of the navier stokes equations with the condition on the pressure on parts of the boundary the local exact controllability is proved by using a global carleman inequality and an estimate of an equation adjoint to a linearized navier stokes equation with the nonstandard boundary condition we also obtain the null controllability of the linearized system by controls acting on an arbitrarily given subdomain

superunitary reduction of the orthosymplectic supertableaux the supertableaux of the orthosymplectic groups osp 2 2p and osp 2 1 2p are decomposed in sums of supertableaux of the superunitary group su p

a non steady system with friction boundary conditions for flow of heat conducting incompressible viscous fluids abstract in this paper we are concerned with a non steady system for motion of incompressible viscous newtonian heat conducting fluids under mixed boundary conditions the boundary conditions for fluid may include tresca slip leak and one sided leak conditions based on total stress velocity total pressure rotation total stress together and the conditions for temperature may include dirichlet neumann and robin conditions together relying on the relations among strain rotation normal derivative of velocity and shape of boundary surface we get variational formulation the formulation consists of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature we first study existence estimation and relative compactness of solutions to an approximate equation by passing to limits as the parameter for approximation goes to zero we get existence of a solution with defect measure for temperature

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

a priori and a posteriori error analysis of a mixed scheme for the brinkman problem this paper deals with the analysis of new mixed finite element methods for the brinkman equations formulated in terms of velocity vorticity and pressure employing the babuska brezzi theory it is proved that the resulting continuous and discrete variational formulations are well posed in particular we show that raviart thomas elements of order k ge 0 k 0 for the approximation of the velocity field piecewise continuous polynomials of degree k 1 k 1 for the vorticity and piecewise polynomials of degree k for the pressure yield unique solvability of the discrete problem on the other hand we also show that families of finite elements based on brezzi douglas marini elements of order k 1 k 1 for the approximation of velocity piecewise continuous polynomials of degree k 2 k 2 for the vorticity and piecewise polynomials of degree k for the pressure ensure the well posedness of the associated galerkin scheme we note that these families provide exactly divergence free approximations of the velocity field we establish a priori error estimates in the natural norms with constants independent of the viscosity and we carry out the reliability and efficiency analysis of a residual based a posteriori error estimator finally we report several numerical experiments illustrating the behaviour of the proposed schemes and confirming our theoretical results on unstructured meshes additional examples of cases not covered by our theory are also presented

modulated traveling fronts for a nonlocal fisher kpp equation a dynamical systems approach abstract we consider a nonlocal generalization of the fisher kpp equation in one spatial dimension as a parameter is varied the system undergoes a turing bifurcation we study the dynamics near this turing bifurcation our results are two fold first we prove the existence of a two parameter family of bifurcating stationary periodic solutions and derive a rigorous asymptotic approximation of these solutions we also study the spectral stability of the bifurcating stationary periodic solutions with respect to almost co periodic perturbations second we restrict to a specific class of exponential kernels for which the nonlocal problem is transformed into a higher order partial differential equation in this context we prove the existence of modulated traveling fronts near the turing bifurcation that describe the invasion of the turing unstable homogeneous state by the periodic pattern established in the first part both results rely on a center manifold reduction to a finite dimensional ordinary differential equation

existence of the solution to stationary navier stokes equations with nonlinear slip boundary conditions abstract the stationary navier stokes equations with nonlinear slip boundary conditions are investigated in this paper because the boundary conditions include the subdifferential property on the part boundary the variational formulation of this problem is the variational inequality problem of the second kind with navier stokes operator the main purpose of the paper is to study the existence of the weak solution and the strong solution to this variational inequality problem in terms of the yosida s regularity method

3d unsteady navier stokes problem with memory and subdifferential boundary condition abstract we consider a mathematical model which describes the motion of a 3d unsteady fluid flow governed by the navier stokes system and subjected to mixed boundary conditions with a given velocity on one part of the boundary and nonlinear slip conditions with a memory term reminiscent of coulomb s friction law on the other part we establish first some regularity properties and estimates for a simplified model then we prove the existence of a solution to our problem by using a successive approximation technique and compactness arguments based on helly s theorem for the velocity field

two grid mfeas for the incompressible stokes type variational inequality with damping abstract in this paper we study two grid mixed finite element algorithms mfeas for the stationary incompressible stokes equations with damping and nonlinear slip boundary conditions we set up the weak formulation and obtain the well posedness then employing the mixed finite element method some optimal error estimates between the exact solution and the approximation solution are derived two kinds of two grid mfeas based on the stokes correction and newton type correction are established some error estimates for two grid mfeas are obtained several numerical results are presented to confirm our theoretical findings

existence of pulses in excitable media with nonlocal coupling abstract we prove the existence of fast traveling pulse solutions in excitable media with non local coupling existence results had been known until now in the case of local diffusive coupling and in the case of a discrete medium with finite range non local coupling our approach replaces methods from geometric singular perturbation theory that had been crucial in previous existence proofs by a pde oriented approach relying on exponential weights fredholm theory and commutator estimates

pressure projection stabilized finite element method for stokes problem with nonlinear slip boundary conditions in this paper we consider the pressure projection stabilized finite element method for the stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the stokes operator the h 1 and l 2 error estimates for the velocity and the l 2 error estimate for the pressure are obtained finally the numerical results are displayed to verify the theoretical analysis

a coherent analysis of stokes flows under boundary conditions of friction type this paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type which are certain nonlinear boundary conditions similar to the so called signorini boundary condition in elasticity we assume that the flow is governed by the linear stokes equation while the boundary condition is nonlinear from the methodological viewpoint the analysis is carried out in a coherent way starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory from the viewpoint of applications we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value

on a strong solution of the non stationary navier stokes equations under slip or leak boundary conditions of friction type abstract strong solutions of the non stationary navier stokes equations under non linearized slip or leak boundary conditions are investigated we show that the problems are formulated by a variational inequality of parabolic type to which uniqueness is established using galerkin s method and deriving a priori estimates we prove global and local existence for 2d and 3d slip problems respectively for leak problems under no leak assumption at t 0 we prove local existence in 2d and 3d cases compatibility conditions for initial states play a significant role in the estimates

spatially structured activity in synaptically coupled neuronal networks i traveling fronts and pulses we consider traveling front and pulse solutions to a system of integro differential equations used to describe the activity of synaptically coupled neuronal networks in a single spatial dimension our first goal is to establish a series of direct links between the abstract nature of the equations and their interpretation in terms of experimental findings in the cortex and other brain regions this is accomplished first by presenting a biophysically motivated derivation of the system and then by establishing a framework for comparison between numerical and experimental measures of activity propagation speed our second goal is to establish the existence of traveling pulse solutions using more rigorous methods two techniques are presented the first a shooting argument reduces the problem from finding a specific solution to an integro differential equation system to finding any solution to an ode system the second a singular perturbation argument provides a construction of traveling pulse solutions un

young supertableaux of the basic lie superalgebras among the simple lie superalgebras lsa the basic classical ones are well known together with many of their finite dimensional representations this is particularly true for the typical representations which are known to be completely reducible it is well known that reducible but indecomposable representations of the basic lsa are not completely characterised by their highest weight hw or the eigenvalues of their casimir operators in fact there may be several different finite representations characterised by the same hw such representations are called non typical or atypical the aim of this paper is to establish a complete characterisation of the typical and non typical representations by means of properly defined young supertableaux yst therefore the definition we are going to use for our yst differs slightly from the standard definitions the examples given throughout this paper help the illustration of this new interpretation for the yst which makes possible the complete classification of the indecom posable representations characterised by a generalised notion of hw

semi discrete stabilized finite element methods for navier stokes equations with nonlinear slip boundary conditions based on regularization procedure based on the pressure projection stabilized methods the semi discrete finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions is considered in this paper because this class of boundary condition includes the subdifferential property then the variational formulation is the navier stokes type variational inequality problem using the regularization procedure we obtain a regularized problem and give the error estimate between the solutions of the variational inequality problem and the regularized problem with respect to the regularized parameter varepsilon which means that the solution of the regularized problem converges to the solution of the navier stokes type variational inequality problem as the parameter varepsilon longrightarrow 0 moreover some regularized estimates about the solution of the regularized problem are also derived under some assumptions about the physical data the pressure projection stabilized finite element methods are used to the regularized problem and some optimal error estimates of the finite element approximation solutions are derived

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

a local regularization operator for triangular and quadrilateral finite elements this paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes this operator is a variant of the regularization operator of clement however ours is constructed via a local projection in a reference domain we prove in this paper that it has the same optimal approximation properties as the standard interpolation operator and we present some applications

some properties on the surfaces of vector fields and its application to the stokes and navier stokes problems with mixed boundary conditions abstract in this paper we are concerned with the stationary and non stationary stokes and navier stokes problems with mixed boundary conditions involving velocity pressure rotation stress and normal derivative of velocity together relying on the relations among strain rotation normal derivative of velocity and shape of boundary surface we get variational formulations of the stokes and navier stokes problems with the mixed boundary conditions also we study existence and uniqueness of solutions to the problems

consistency stability a priori and a posteriori errors for petrov galerkin methods applied to nonlinear problems in an abstract framework we present a formalism which specifies the notions of consistency and stability of petrov galerkin methods used to approximate nonlinear problems which are in many practical situations strongly nonlinear elliptic problems this formalism gives rise to a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods applied to elliptic nonlinear problems this theory is illustrated with the example div k u u c u f in a two dimensional domain with dirichlet boundary conditions

numerical analysis of a characteristic stabilized finite element method for the time dependent navier stokes equations with nonlinear slip boundary conditions abstract based on a characteristic method this work is concerned with a finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions since this slip boundary condition of friction type contains a subdifferential property its continuous variational problem is formulated as an inequality which can turn into an equality problem by using a powerful regularized method then a fully discrete characteristic scheme under the stabilized lower order finite element pairs is proposed for the equality problem optimal error estimates for velocity and pressure are derived under the corresponding l 2 h 1 norms finally a smooth problem test is reported to demonstrate the theoretically predicted convergence order and the expected slip phenomena and the simulation of a bifurcated blood flow model is displayed to illustrate the efficiency of the proposed method

on korn s first inequality with non constant coefficients in this paper we prove a korn type inequality with non constant coefficients which arises from applications in elasto plasticity at large deformations more precisely let r 3 be a bounded lipschitz domain and let be a smooth part of the boundary with non vanishing two dimensional lebesgue measure define and let be given with det f p x 0 moreover suppose that rot then clearly this result generalizes the classical korn s first inequality which is just our result with f p 11 with slight modifications we are also able to treat forms of the type

steady flow of generalized newtonian fluid with multivalued rheology and nonmonotone friction law abstract we study the stationary incompressible flow of a generalized newtonian fluid described by a nonlinear multivalued maximal monotone constitutive law and a multivalued nonmonotone frictional boundary condition we provide results on the existence and uniqueness of a solution to the variational form of the problem when the multivalued laws are of a subdifferential form we prove the existence of a solution to a variational hemivariational inequality for the flow s velocity field

mixed boundary value problems for the stokes system we prove the well posedness of the mixed problem for the stokes system in a class of lipschitz domains in n n 3 the strategy is to reduce the original problem to a boundary integral equation and we establish certain new rellich type estimates which imply that the intervening boundary integral operator is semi fredholm we then prove that its index is zero by performing a homotopic deformation of it onto an operator related to the lame system which has recently been shown to be invertible

representations of the superalgebra f4 and young supertableaux the authors present a method for constructing typical as well as atypical finite dimensional representations of the superalgebra f4 for such a purpose young supertableaux are introduced