vanishing viscosity with short wave long wave interactions for multi d scalar conservation laws we consider a system coupling a multidimensional semilinear schrodinger equation and a multidimensional nonlinear scalar conservation law with viscosity which is motivated by a model of short wave long wave interaction introduced by benney 1977 we prove the global existence and uniqueness of the solution of the cauchy problem for this system we also prove the convergence of the whole sequence of solutions when the viscosity e and the interaction parameter approach zero so that o e1 2 we also indicate how to extend these results to more general systems which couple multidimensional semilinear systems of schrodinger equations with multidimensional nonlinear systems of scalar conservation laws mildly coupled

optimal bounds for a lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions optimal bounds for a lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

renormalized entropy solutions of scalar conservation laws with boundary condition we study an initial boundary value problem for a scalar conservation law u t div phi u f on a bounded domain existence and uniqueness of a renormalized entropy solution is established for general l 1 data phi is an element ofc r r n

measure valued solutions to initial boundary value problems for certain systems of conservation laws existence and dynamics a framework for studying initial boundary value problems for systems of conservation laws in what concerns to the existence of measure valued solutions and their asymptotic behavior is developed here with the helpful introduction of a class of flux maps which allow a rather complete treatment of these questions including systems of practical importance as those arising in multiphase flow in porous media the systems of this class may in general admit umbilic points submanifolds where genuine nonlinearity fails as well as elliptic regions we prove the existence of measure valued solutions by using the vanishing viscosity method and also finite difference schemes the main result about the dynamics of the measure valued solutions is that for certain special boundary values given by constant states the time averages of these m v solutions converge weakly to the dirac measure concentrated at those states for a e space variable the rate of convergence of the time averages of the expected values can be estimated by properties of the flux maps only

the small dispersion limit of the korteweg de vries equation iii in parts i and ii we have derived explicit formulas for the distribution limit u of the solution of the kdv equation as the coefficient of uxxx tends to zero this formula contains n parameters 1 n whose values as well as whose number depends on x and t in section 4 we have shown that for t tb n 1 and the value of was determined in section 5 we have shown that the parameters i satisfy a nonlinear system of partial differential equations in part iii section 6 we show that for t large n 3 and we determine the asymptotic behavior of 1 2 3 and of u and u2 for t large the explicit formulas show that u and u2 are o t 1 and o t 2 respectively see formulas 6 2 and 6 24 in section 7 we study initial data whose value tends to zero as x and to 1 as x if one accepts some plausible guesses about the behavior of solutions with such initial data we derive an explicit formula for the solution and determine the large scale asymptotic behavior of the solution the function s is expressible in terms of complete elliptic integrals a similar formula is derived for u2 in section 8 we indicate how to extend the treatment of this series of papers to multihumped but still negative initial data

quasiconvex elastodynamics weak strong uniqueness for measure valued solutions a weak strong uniqueness result is proved for measure valued solutions to the system of conservation laws arising in elastodynamics the main novelty brought forward by the present work is that the underlying stored energy function of the material is assumed strongly quasiconvex the proof employs tools from the calculus of variations to establish general convexity type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

on the dirichlet problem for first order quasilinear equations on a manifold we study the dirichlet problem for a first order quasilinear equation on a smooth manifold with boundary existence and uniqueness of a generalized entropy solution are established the uniqueness is proved under some additional requirement on the field of coefficients it is shown that generally the uniqueness fails the non uniqueness occurs because of presence of the characteristics not outgoing from the boundary including closed ones the existence is proved in general case moreover we establish that among generalized entropy solutions laying in the ball u r there exist the unique maximal and minimal solutions to prove our results we use the kinetic formulation similar to one by c imbert and j vovelle introduction let m be a n dimensional c smooth compact manifold with boundary s m thus in a neighborhood of each point x0 m we can define the local coordinates x1 xn j x x u corresponding to the chart u j v where u is a neighborhood of the point x0 coordinate neighborhood v is an open subset of the half space x x1 xn r x1 0 x x2 xn rn 1 and j u v is a c diffeomorphism clearly boundary points of u and v must correspond each other under the diffeomorphism j j u s v denote by tm t m the tangent and cotangent bundles on m and by txm t xm the corresponding fibres of these bundles at a point x m any vector field a a x txm being a section of the tangent bundle tm acts on smooth functions f x c m as a first order differential operator represented in local coordinates x1 xn as a a x xi i e a f ai x xi

existence and asymptotic behavior of measure valued solutions for degenerate conservation laws abstract we consider two classes of typical degenerate hyperbolic systems of conservation laws to provide a general approach for solving the existence and large time asymptotic behavior of measure valued solutions for initial boundary value problems some existence theorems of the measure valued solutions are established the convergence of large time averages of the measure valued solutions to a dirac mass concentrated at the input state on the boundary is proved for almost each fixed space variable although the measure valued solutions of the initial boundary problems may not be unique in general our results indicate that the asymptotic equilibrium of these measure valued solutions is unique

dynamic spectral shape features as acoustic correlates for initial stop consonants a comprehensive investigation of two acoustic feature sets for english stop consonants spoken in syllable initial position was conducted to determine the relative invariance of the features that cue place and voicing the features evaluated were overall spectral shape encoded as the cosine transform coefficients of the nonlinearly scaled amplitude spectrum and formants in addition features were computed both for the static case i e from one 25 ms frame starting at the burst and for the dynamic case i e as parameter trajectories over several frames of speech data all features were evaluated with speaker independent automatic classification experiments using the data from 15 speakers to train the classifier and the data from 15 different speakers for testing the primary conclusions from these experiments as measured via automatic recognition rates are as follows 1 spectral shape features are superior to both formants and formants plus amplitudes 2 features extracted from the dynamic spectrum are superior to features extracted from the static spectrum and 3 features extracted from the speech signal beginning with the burst onset are superior to features extracted from the speech signal beginning with the vowel transition dynamic features extracted from the smoothed spectra over a 60 ms interval timed to begin with the burst onset appear to account for the primary vowel context effects automatic recognition results for the 6 stops 93 7 based on 20 features was better than the rates obtained with human listeners for a 50 ms segment 89 9 and only slightly worse than the rates obtained by human listeners for a 100 ms interval 96 6 thus the basic conclusion from our work is that dynamic spectral shape features are acoustically invariant cues for both place and voicing in initial stop consonants

evaluation of inverse fourier transforms through romberg integration this study deals with evaluation of inverse integral transforms through numerical integration arguments are presented to explain that such a numerical evaluation is mathematically incorrect in recent years a sudden increase has been noticed in the number of research publications in which romberg integration is said to have used in evaluating the inverse fourier transforms in this regard even the references cited in these papers do not support such an evaluation but suggest contrary an immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

interactions due to mechanical thermal sources in a micropolar thermoelastic medium possessing cubic symmetry abstract the present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface analytic expressions for displacement components microrotation force stress couple stress and temperature distribution are obtained in the physical domain for lord shulman l s and green lindsay g l theories of thermoelasticity by applying integral transforms a numerical inversion technique has been applied to obtain the solution in the physical domain the numerical results are presented graphically for a particular model

measure valued solutions to conservation laws motivated by traffic modelling motivated by a traffic model we study a conservation law whose solutions naturally need to be bounded radon measures we investigate the relations between this equation and finite systems of conservation laws that converge to it

finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws we develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms the schemes are of equilibrium type hence with uniform bounds on approximate solutions valid in cell entropy inequalities and exact for some equilibrium states convergence is investigated in the framework of kinetic schemes numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms equilibrium type schemes produce accurate results even on test problems for which the standard approach fails for some numerical tests they exhibit exponential type convergence rate in two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 50002 grid points

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

young measure solutions for a viscoelastically damped wave equation with nonmonotone stress strain relation we study the viscoelastically damped wave equation with a nonmonotone stress strain relation this system describes the dynamics of phase transitions which is closely related to the creation of microstructures in order to analyze the dynamic behavior of microstructures we consider highly oscillatory initial states two questions are addressed in this work how do oscillations propagate in space and time what can be said about the long time behavior an appropriate tool to deal with oscillations are young measures they describe the local distribution or one point statistics of a sequence of fast fluctuating functions we demonstrate that highly oscillatory initial states generate in a unique fashion an evolution in the space of young measures and we derive the determining equations further on we prove a generalized dissipation identity for young measure solutions as a consequence it is shown that every low energy solution converges to a young measure equilibrium as t this is a generalization of g friesecke s j b mcleod s fm96 convergence result for classical solutions to the case of young measure solutions

multi dimensional scalar balance laws with discontinuous flux abstract we consider scalar balance laws with a dissipative source term the flux function may be discontinuous with respect to both the space variable x and the unknown quantity u we formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem the problem is formulated in the framework of multi valued mappings the notion of entropy measure valued solutions is used to prove the so called contraction principle and comparison principle

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

a new convergence proof for finite volume schemes using the kinetic formulation of conservation laws we give a new convergence proof for finite volume schemes approximating scalar conservation laws the main ingredients of the proof are the kinetic formulation of scalar conservation laws a discrete entropy inequality and the velocity averaging technique

well posedness theory for degenerate parabolic equations on riemannian manifolds abstract we consider the degenerate parabolic equation t u div f x u div div a x u x m t 0 on a smooth compact d dimensional riemannian manifold m g here for each u r x f x u is a vector field and x a x u is a 1 1 tensor field on m such that u a x u t x m is non decreasing with respect to u the fact that the notion of divergence appearing in the equation depends on the metric g requires revisiting the standard entropy admissibility concept we derive it under an additional geometry compatibility condition and as a corollary we introduce the kinetic formulation of the equation on the manifold using this concept we prove well posedness of the corresponding cauchy problem

the zero dispersion limit of the korteweg de vries equation for initial potentials with non trivial reflection coefficient the inverse scattering method is used to determine the distribution limit as 0 of the solution u x t of the initial value problem ut 6uux 2uxxx 0 u x 0 v x where v x is a positive bump which decays sufficiently fast as x x the case v x 0 has been solved by peter d lax and c david levermore 8 9 10 the computation of the distribution limit of u x t as 0 is reduced to a quadratic maximization problem which is then solved

multiscale young measures in homogenization of continuous stationary processes in compact spaces and applications abstract we introduce a framework for the study of nonlinear homogenization problems in the setting of stationary continuous processes in compact spaces the latter are functions f t r n q q with f t x f t x where q is a compact hausdorff topological space f c q and t x q q x r n is an n dimensional continuous dynamical system endowed with an invariant radon probability measure it can be easily shown that for almost all q the realization f t x belongs to an algebra with mean value that is an algebra of functions in buc r n containing all translates of its elements and such that each of its elements possesses a mean value this notion was introduced by zhikov and krivenko v v zhikov e v krivenko homogenization of singularly perturbed elliptic operators mat zametki 33 1983 571 582 english transl in math notes 33 1983 294 300 we then establish the existence of multiscale young measures in the setting of algebras with mean value where the compactifications of r n provided by such algebras plays an important role these parametrized measures are useful in connection with the existence of correctors in homogenization problems we apply this framework to the homogenization of a porous medium type equation in r n with a stationary continuous process as a stiff oscillatory external source this application seems to be new even in the classical context of periodic homogenization

on the strong pre compactness property for entropy solutions of a degenerate elliptic equation with discontinuous flux abstract under some non degeneracy condition we show that sequences of entropy solutions of a semi linear elliptic equation are strongly pre compact in the general case of a caratheodory flux vector the proofs are based on localization principles for h measures corresponding to sequences of measure valued functions

locus equations as phonetic descriptors of consonantal place of articulation this experiment tested whether locus equation coefficients slope and y intercept could serve as indices of place of articulation for obstruents sharing the same place of articulation across different manner classes a previous study c a fowler percept psychophys 55 597 610 1994 reported that locus equations provided poor information for place because the mean slope for d 0 47 was found to be statistically different than the mean slope for z 0 42 across ten speakers locus equations from 22 speakers were derived from cv t words with initial voiced oral stop d voiceless aspirated stop th nasal stop n voice fricative z and voiceless fricative s preceding ten vowel contexts post hoc tests revealed d z n for slope means slopes for d and th were also equivalent when f2 onset measurement points were corrected to account for aspiration scatterplots of slopes y intercepts revealed three nonoverlapping and distinct clusters of coordinates when the coronal group d t n z s was plotted versus labials and velars a discriminant analysis using slope and y intercept successfully categorized all coronals as alveolars with 87 1 accuracy the collective results support the contention that locus equations can serve as effective descriptors of consonant place of articulation across manner classes work supported by nih

locus equations derived from compensatory articulation locus equations are linear regressions of the onset of f2 transitions on their offsets these functions vowel normalize the f2 transitions such that they are able to characterize consonantal place categories the purpose of this research was to determine if compensatory articulation due to bite blocks would alter the normally linear relationship between f2 transition onset and offset frequencies or alter the differential slopes and y intercepts of locus equations as a function of stop place six speakers three male and three female each produced bvt dvt and gvt tokens for ten vowel contexts under normal and bite block conditions extremely linear and practically identical scatterplots were obtained in the two speaking conditions no adaptation to the bite blocks was found when comparing locus equations derived from the initial versus the final bite block trial results are discussed in relation to the orderly output constraint which postulates a perceptual function for linearly related f2 transition end points within consonantal place categories

finite volume relaxation schemes for multidimensional conservation laws we consider finite volume relaxation schemes for multidimensional scalar conservation laws these schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h 1 4 in l 0 t l loc 1 r d

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws we consider initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws through the scalar case the entropy solutions we address assume their initial data only in the sense of weak star in l as t 0 and satisfy the entropy inequality in the sense of distributions for t 0 we prove that if the flux function has weakly genuine nonlinearity then the entropy solutions are always unique and the initial layers do not appear we also discuss applications to the zero relaxation limit for hyperbolic systems of conservation laws with relaxation

an investigation of locus equations as a source of relational invariance for stop place categorization locus equations were investigated as a potential metric capable of illustrating relational invariance for place of articulation in voiced initial stop consonants independently of vowel context locus equations are straight line regression fits to data points formed by plotting onsets of f2 transitions along the y axis and their corresponding midvowel nuclei along the x axis twenty subjects 10 male and 10 female produced b v t d v t and g v t tokens for ten vowel contexts each cvc token was repeated in a carrier phrase five times yielding 50 tokens per stop place category formant measures were obtained using the macspeech lab ii speech analysis system extremely linear regression functions were found characterized by distinct slopes and y intercepts as a function of place of articulation a discriminant analysis using f2onset and vowel frequencies as predictors showed 82 78 and 67 classification rates for labial alveolar and velar place using derived slope and y intercept values as predictors led to 100 classification into stop place categories a neurobiologically oriented perspective on the invariance issue is developed and a brain based recognition algorithm for stop place integrating burst and f2 trajectory cues is offered

existence and asymptotic behavior of measure valued solutions for three phase flow in porous media abstract we establish the existence of physically admissible measure valued solutions for the initial boundary value problem modelling the bow of water gas and oil in a one dimensional reservoir under water flooding and we prove the convergence of the time averages of the expected values for the saturations of water and gas to the state which represents pure water at a rate which depends only on the shape of the flux functions near this state we also present some useful general results about the weak convergence of probability measures to dirac measures

convergence of a residual based artificial viscosity finite element method we present a residual based artificial viscosity finite element method to solve conservation laws the galerkin approximation is stabilized by only residual based artificial viscosity without any least squares supg or streamline diffusion terms we prove convergence of the method applied to a scalar conservation law in two space dimensions toward an unique entropy solution for implicit time stepping schemes

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

weak asymptotic decay via a relaxed invariance principle for a wave equation with nonlinear non monotone damping this paper considers the problem of asymptotic decay as t of solutions of the wave equation u tt u a x u t u t x a bounded open connected set in n n 1 with smooth boundary u 0 on the nonlinear function is not assumed to be globally lipschitz continuous 0 y 2 y n 1 0 y 1 y 1 y n 1 0 for all y n 1 is not assumed to be monotone in y 1 under additional restrictions on the kernel of conditions are given which imply that u u t converges to 0 0 weakly in h h 1 0 l 2 as t the work generalises earlier results of dafermos and haraux where strong decay in h as t was obtained in the case y 1 y n 1 q y 1 q monotone on

a new version of the two dimensional lax friedrichs scheme we develop a new two dimensional version of the lax friedrichs scheme which corresponds exactly to a transport projection method the scheme we obtain in this way is different from the one derived by averaging the one dimensional scheme in the two directions as usually done the laxfriedrichs scheme is known to be a very stable scheme with much diffusion however this diffusion can be easily reduced by using corrected fluxes without altering the total variation estimates the accuracy of this corrected scheme is of order two except near a local extrema the numerical results computed by using this corrected scheme are similar to the ones obtained by using the godunov scheme with corrected fluxes but require less cpu time convergence towards the entropy solution is proved and some extensions to systems of conservation laws or three dimensional models are discussed some numerical experiments are reported

multiscale young measures in almost periodic homogenization and applications we prove the existence of multiscale young measures associated with almost periodic homogenization we give applications of this tool in the homogenization of nonlinear partial differential equations with an almost periodic structure such as scalar conservation laws nonlinear transport equations hamilton jacobi equations and fully nonlinear elliptic equations motivated by the application in nonlinear transport equations we also prove basic results on flows generated by lipschitz almost periodic vector fields which are of interest in their own in our analysis an important role is played by the so called bohr compactification mathbb g n of mathbb r n this is a natural parameter space for the young measures our homogenization results provide also the asymptotic behavior for the whole set of mathbb g n translates of the solutions which is in the spirit of recent studies on the homogenization of stationary ergodic processes

kinetic decomposition for singularly perturbed higher order partial differential equations abstract in this paper we consider singularly perturbed higher order partial differential equations we establish the condition under which the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed in hwang and tzavaras comm partial differential equations 27 2002 1229 first we obtain the approximate transport equation for the given dispersive equations then using the averaging lemma we obtain the convergence

young measures generated by ideal incompressible fluid flows in their seminal paper diperna and majda commun math phys 108 4 667 689 1987 introduced the notion of a measure valued solution for the incompressible euler equations in order to capture complex phenomena present in limits of approximate solutions such as persistence of oscillation and development of concentrations furthermore they gave several explicit examples exhibiting such phenomena in this paper we show that any measure valued solution can be generated by a sequence of exact weak solutions in particular this gives rise to a very large arguably too large set of weak solutions of the incompressible euler equations

formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary we study nonlinear hyperbolic conservation laws posed on a differential n 1 manifold with boundary referred to as a spacetime and defined from a prescribed flux field of n forms depending on a parameter the unknown variable a class of equations proposed by lefloch and okutmustur far east j math sci 31 49 83 2008 our main result is a proof of the convergence of the finite volume method for weak solutions satisfying suitable entropy inequalities a main difference with previous work is that we allow for slices with a boundary and in addition introduce a new formulation of the finite volume method involving the notion of total flux functions under a natural global hyperbolicity condition on the flux field and the spacetime and by assuming that the spacetime admits a foliation by compact slices with boundary we establish an existence and uniqueness theory for the initial and boundary value problem and we prove a contraction property in a geometrically natural l 1 type distance

a cross linguistic investigation of locus equations as a phonetic descriptor for place of articulation a previous study h sussman h mccaffrey and s matthews j acoust soc am 90 1309 1325 1991 of american english cv coarticulation showed a remarkably linear relationship between onset frequencies of f2 transitions plotted on the y axis in relation to the f2 midvowel target frequencies plotted on the x axis for cvc tokens with initial b d g and ten medial vowel contexts slope and y intercept values of regression functions fit to these scatterplots locus equations were shown to serve as statistically powerful phonetic descriptors of place of articulation the present study extends the locus equation metric to three additional languages thai cairene arabic and urdu having both two and four place contrasts for syllable initial voiced stops a total of 14 speakers thai 6 arabic 3 urdu 5 produced 1740 cvc tokens that were acoustically analyzed using macspeech lab ii strong linear regression relationships were found for every stop category across all speakers slopes and y intercepts systematically varied as a function of place of articulation cross language comparisons of stop place categories were performed but variability of slope and y intercept means tempered conclusions concerning the existence of cv phonetic hot spots

statistical solutions and onsager s conjecture abstract we prove a version of onsager s conjecture on the conservation of energy for the incompressible euler equations in the context of statistical solutions as introduced recently by fjordholm et al 2017 as a byproduct we also obtain an alternative proof for the conservative direction of onsager s conjecture for weak solutions under a weaker besov type regularity assumption than previously known

a hybrid lagrangian model based on the aw rascle traffic flow model in this paper we propose a simple fully discrete hybrid model for vehicular traffic flow for which both the macroscopic and the microscopic models are based on a lagrangian discretization of the aw rascle ar model a aw and m rascle siam j appl math 60 2000 pp 916 938 this hybridization makes use of the relation between the ar macroscopic model and a follow the leader type model d c gazis r herman and r w rothery oper res 9 1961 pp 545 567 r herman and i prigogine kinetic theory of vehicular traffic american elsevier new york 1971 established in a aw a klar m materne and m rascle siam j appl math 63 2002 pp 259 278 moreover in the hybrid model the total variation in space of the velocity v is nonincreasing the total variation in space of the specific volume tau is bounded and the total variations in time of v and tau are bounded finally we present some numerical simulations which confirm that the models synchronization processes do

scalar conservation laws on constant and time dependent riemannian manifolds abstract in this paper we establish well posedness for scalar conservation laws on closed manifolds m endowed with a constant or a time dependent riemannian metric for initial values in l m in particular we show the existence and uniqueness of entropy solutions as well as the l 1 contraction property and a comparison principle for these solutions throughout the paper the flux function is allowed to depend on time and to have non vanishing divergence furthermore we derive estimates of the total variation of the solution for initial values in bv m and we give in the case of a time independent metric a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates

erratum to existence and strong pre compactness properties for entropy solutions of a first order quasilinear equation with discontinuous flux sequences of entropy solutions of a non degenerate first order quasilinear equation are shown to be strongly pre compact in the general case of a caratheodory flux vector existence of the weak and entropy solution to the cauchy problem for such an evolutionary equation is also established the proofs are based on the general localization principle for h measures corresponding to sequences of measure valued functions