structural measurement errors in nonseparable models this paper considers measurement error from a new perspective in surveys response errors are often caused by the fact that respondents recall past events and quantities imperfectly we explore the consequences of limited recall for the identification of marginal effects our identification approach is entirely nonparametric using matzkin type nonseparable models that nest a large class of potential structural models we show that measurement error due to limited recall will generally exhibit nonstandard behavior in particular be nonclassical and differential even for left hand side variables in linear models we establish that information reduction by individuals is the critical issue for the severity of recall measurement error in order to detect information reduction we propose a nonparametric test statistic finally we propose bounds to address identification problems resulting from recall errors we illustrate our theoretical findings using real world data on food consumption

goodness of fit tests for kernel regression with an application to option implied volatilities this paper proposes a test of a restrictedspeci cation of regression basedon comparing residual sum of squares from kernel regression our main case is where both the restrictedspeci cation andthe general mod el are nonparametric with our test equivalently viewed as a test of dimension reduction we discuss practical features of implementing the test andvariations applicable to testing parametric mod els as the null hypothesis or semiparametric models that depend on a nite parameter vector as well as unknown functions we apply our testing procedure to option prices we reject a parametric version of the black scholes formula but fail to reject a semiparametric version against a general nonparametric regression 2001 elsevier science s a all rights reserved jel classi cation c12 c14

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

equivalence of the euler and lagrangian equations of gas dynamics for weak solutions abstract this paper demonstrates the equivalence of the euler and the lagrangian equations of gas dynamics in one space dimension for weak solutions which are bounded and measurable in eulerian coordinates the precise hypotheses include all known global solutions on r r in particular solutions containing vacuum states zero mass density are included furthermore there is a one to one correspondence between the convex extensions of the two systems and the corresponding admissibility criteria are equivalent in the presence of a vacuum the definition of weak solution for the lagrangian equations must be strengthened to admit test functions which are discontinuous at the vacuum as an application we translate a large data existence result of diperna for the euler equations for isentropic gas dynamics into a similar theorem for the lagrangian equations

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

a functional integral approach to shock wave solutions of the euler equations with spherical symmetry ii abstract this is a continuation of 15 as is well known one dimensional conservation laws without source term have been extensively investigated after the foundamental paper of j glimm 3 and those with integrable source terms were solved by liu 6 7 etc for higher dimensional case with spherical symmetry makino 8 first proved a linear growth rate for solutions when p 2 where 1 but in order to get global existence for 1 and the decay property we need to find a uniform bound for the approximate solutions in 15 we introduced a new norm and a functional integral approach to prove a uniform bound for a model problem of euler equation in r 3 with spherical symmetry in order to overcome the geometric effects of spherical symmetry which leads to a non integrable source term we considered an infinite reflection problem and solved it by considering the cancellations between reflections of different orders in this paper we consider a system which describes the isentropic and spherically symmetric motion of gas flow surrounding a solid star with radius 1 and mass m it is interesting to note that the wave curves for this problem are no longer continuous and there is an extra term in the wave interaction estimates by introducing a new norm we prove a similar result as 15 in the appendix we present a local existence theorem for 1 which was also obtained by makino 9 by different method and we extend the results to the cases with different boundary conditions

convergence of shock capturing schemes for the compressible euler poisson equations we are concerned with approximate methods to construct global solutions with geometrical structure to the compressible euler poisson equations in several space variables a shock capturing numerical scheme is introduced to overcome the new difficulties from the nonlinear resonance of the system and the nonlocal behavior of the source terms the convergence and consistency of the shock capturing scheme for the equations is proved with the aid of the compensated compactness method then new existence results of the global solutions with geometrical structure are obtained the traces of the weak solutions are defined and then the weak solutions are proved to satisfy the boundary conditions the initial data are arbitrarily large withl bounds

symmetries and global solvability of the isothermal gas dynamics equations we study the cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics in which the pressure and the density are related by the law equation p with 1 our results complete those obtained earlier for 1 we prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method the proof relies on compensated compactness arguments and symmetry group analysis interestingly we make use here of the fact that the isothermal gas dynamics system is invariant modulo a linear scaling of the density this property enables us to reduce our problem to that with a small initial density

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

a note on the blowup criterion of the lagrangian averaged euler equations abstract in this note we consider the existence of the 3d lagrangian averaged euler equations we obtain local existence in w s p and a sufficient condition for the global existence

singular limits of stiff relaxation and dominant diffusion for nonlinear systems abstract we are concerned with singular limits of stiff relaxation and dominant diffusion for general 2 2 nonlinear systems of conservation laws that is the relaxation time tends to zero faster than the diffusion parameter e o e e 0 we establish the following general framework if there exists an a priori l bound that is uniformly with respect to e for the solutions of a system then the solution sequence converges to the corresponding equilibrium solution of this system our results indicate that the convergent behavior of such a limit is independent of either the stability criterion or the hyperbolicity of the corresponding inviscid quasilinear systems which is not the case for other type of limits this framework applies to some important nonlinear systems with relaxation terms such as the system of elasticity the system of isentropic fluid dynamics in eulerian coordinates and the extended models of traffic flows the singular limits are also considered for some physical models without l bounded estimates including the system of isentropic fluid dynamics in lagrangian coordinates and the models of traffic flows with stiff relaxation terms the convergence of solutions in l p to the equilibrium solutions of these systems is established provided that the relaxation time tends to zero faster than e

error bounds for finite difference approximations for a class of nonlinear parabolic systems in this paper we establish error bounds for a finite difference approximation to solutions of certain parabolic systems of the form t f po u we assume that the cauchy data is of class bv and we show that the sup norm of the error is bounded by o axiln axi at positive times

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

effective velocity in compressible navier stokes equations with third order derivatives abstract a formulation of certain barotropic compressible navier stokes equations with third order derivatives as a viscous euler system is proposed by using an effective velocity variable the equations model for instance viscous korteweg or quantum navier stokes flows the formulation in the new variable allows for the derivation of an entropy identity which is known as the bd bresch desjardins entropy equation as a consequence of this estimate a new global in time existence result for the one dimensional quantum navier stokes equations with strictly positive particle densities is proved

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

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

convergence of the viscosity solutions for the system of nonlinear elasticity abstract in this paper some special entropy pairs of lax type are constructed for the system of nonlinear elasticity in which the progressive terms are functions of a single variable the necessity estimates for the major terms are obtained by using the theory of singular perturbation of the ordinary differential equations the special entropy pairs are used to prove that the family of young measures uniquely determined by the viscosity solution sequence is a family of dirac measures hence a convergence theorem on the viscosity solutions is established by applying the method of compensated compactness

existence of global bounded weak solutions to nonsymmetric systems of keyfitz kranzer type in this paper we study the global l solutions for the cauchy problem of nonsymmetric system 1 1 of keyfitz kranzer type when n 1 1 1 is the aw rascle traffic flow model first we introduce a new flux approximation to obtain a lower bound e 0 for the parabolic system generated by adding artificial viscosity to the aw rascle system then using the compensated compactness method with the help of l1 estimate of we t x we prove the pointwise convergence of the viscosity solutions under the general conditions on the function p which includes prototype function p 1 a where 1 0 0 a is a constant second by means of bv estimates on the riemann invariants and the compensated compactness method we prove the global existence of bounded entropy weak solutions for the cauchy problem of general nonsymmetric systems 1 1

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

a relaxation theorem and its application to the equilibrium of gases keywords relaxed problem lower convex envelope gas equilibrium van der waal s equation reference caa article 1981 001doi 10 1007 bf00280643view record in web of science record created on 2008 11 25 modified on 2017 05 12

the comparison of the riemann solutions in gas dynamics in this paper we compare two riemann solution constructions of isentropic and nonisentropic gas dynamic equations with the same initial values we obtain that when rarefaction waves occur in the non isentropic solution the same family rarefaction waves occur in the isentropic solution however when advancing or reflected shock waves occur in the isentropic case the same kind shock waves occur in the nonisentropic case moreover by numerical calculation it can be found that the wave intensities of the two solutions are quite close our conclusion reflects that almost non isentropic gas dynamic process can be simulated by isentropic gas dynamic process in practice c 2015 elsevier inc all rights reserved

uniqueness and stability of riemann solutions with large oscillation in gas dynamics we prove the uniqueness of riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 3 system of euler equations in gas dynamics the proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane the uniqueness of riemann solutions yields their inviscid large time stability under arbitrarily large perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation satisfying a natural condition on its growth with time no specific reference to any particular method for constructing the entropy solutions is needed the uniqueness result for riemann solutions can easily be extended to entropy solutions u x t piecewise lipschitz in x for any t 0 with arbitrarily large oscillation

statistical mechanics of the periodic benjamin ono equation the periodic benjamin ono equation is an autonomous hamiltonian system with a gibbs measure on l2 t this paper shows that the gibbs measures on bounded balls of l2 satisfy some logarithmic sobolev inequalities the space of n soliton solutions of the periodic benjamin ono equation as discovered by case is a hamiltonian system with an invariant gibbs measure as n these gibbs measures exhibit a concentration of measure phenomenon case introduced soliton solutions that are parameterized by atomic measures in the complex plane the limiting distributions of these measures give the density of a compressible gas that satisfies the isentropic euler equations the periodic benjamin ono equation is an autonomous hamiltonian system with a gibbs measure on l2 t this paper shows that the gibbs measures on bounded balls of l2 satisfy some logarithmic sobolev inequalities the space of n soliton solutions of the periodic benjamin ono equation as discovered by case is a hamiltonian system with an invariant gibbs measure as n these gibbs measures exhibit a concentration of measure phenomenon case introduced soliton solutions that are parameterized by atomic measures in the complex plane the limiting distributions of these measures give the density of a compressible gas that satisfies the isentropic euler equations

existence of the entropy solution for a viscoelastic model in this paper we consider the cauchy problem for a viscoelastic model with relaxationut x 0 f u t 1 f u 0with discontinuous large initial data where 0 0 are constants when the system is nonstrictly hyperbolic under the additional assumptionv0x l the system is reduced to an inhomogeneous scalar balance law by employing the special form of the system itself after introducing a definition of entropy solutions to the system we prove the existence uniqueness and continuous dependence of the global entropy solution for the system when the system is strictly hyperbolic some special entropy pairs of the lax type are constructed in which the progression terms are functions of a single variable and the necessary estimates for the major terms are obtained by using the theory of singular perturbation of the ordinary differential equations the special entropy pairs are used to prove the existence of the global entropy solutions for the corresponding cauchy problem by applying the method of compensated compactness

viscous limits for piecewise smooth solutions to systems of conservation laws in this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity it is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order e as the viscosity coefficient e goes to zero the proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

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

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

existence of global weak solutions to a special system of euler equation with a source ii general case abstract in this paper we apply the maximum principle and the theory of compensated compactness to establish an existence theorem for global weak solutions to the cauchy problem of the non strictly hyperbolic system a special system of euler equation with a general source term

eulerian droplet model delta shock waves and solution of the riemann problem abstract we study an eulerian droplet model which can be seen as the pressureless gas system with a source term a subsystem of this model and the inviscid burgers equation with source term the condition for loss of regularity of a solution to burgers equation with source term is established the same condition applies to the eulerian droplet model and its subsystem the riemann problem for the eulerian droplet model is constructively solved by going through the solution of the riemann problems for the inviscid burgers equation with a source term and the subsystem respectively under suitable generalized rankine hugoniot relations and entropy condition the existence of delta shock solution is established the existence of a solution to the generalized rankine hugoniot conditions is proven some numerical illustrations are presented

local indirect least squares and average marginal effects in nonseparable structural systems we study the scope of local indirect least squares lils methods for nonparametrically estimating average marginal effects of an endogenous cause x on a response y in triangular structural systems that need not exhibit linearity separability or monotonicity in scalar unobservables one main finding is negative in the fully nonseparable case lils methods cannot recover the average marginal effect lils methods can nevertheless test the hypothesis of no effect in the general nonseparable case we provide new nonparametric asymptotic theory treating both the traditional case of observed exogenous instruments z and the case where one observes only error laden proxies for z

finite energy method for compressible fluids the navier stokes korteweg model this is the first of a series of papers devoted to the initial value problem for the one dimensional euler system of compressible fluids and augmented versions containing higher order terms in the present paper we are interested in dispersive shock waves and analyze the zero viscosity capillarity limit associated with the navier stokes korteweg system specifically we establish the existence of finite energy solutions as well as their convergence toward entropy solutions to the euler system our method of proof combines energy and effective energy estimates a nonlinear sobolev inequality high integrability properties for the mass density and for the velocity and compactness properties based on entropies 2015 wiley periodicals inc

viscous limits for piecewise smooth solutions of the p system abstract we study the zero dissipation problem for a one dimensional model system for the isentropic flow of a compressible viscous gas the so called p system with viscosity when the solution of the inviscid problem is piecewise smooth and having finitely many noninteracting shocks satisfying the entropy condition there exists unique solution to the viscous problem which converges to the given inviscid solution away from shock discontinuities at a rate of order e as the viscosity coefficient e goes to zero the proof is given by a matched asymptotic analysis and an elementary energy method and we do not need the smallness condition on the shock strength

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

hyperbolic conservation laws with umbilic degeneracy i in this paper a compactness framework for approximate solutions to nonlinear hyperbolic systems with umbilic degeneracy is established by combining techniques of compensated compactness with some classical methods and by a detailed analysis of a highly singular equation of euler poisson darboux type then this framework is successfully applied to prove the convergence of the viscosity method and to prove the existence of global entropy solutions for the cauchy problem with large initial data for a canonical class of the systems with quadratic flux form

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

existence of global entropy solutions of a nonstrictly hyperbolic system in this paper we use the theory of compensated compactness coupled with some basic ideas of the kinetic formulation by lions perthame souganidis tadmor lps lpt to establish an existence theorem for global entropy solutions of the nonstrictly hyperbolic system 1

stability and spectral convergence of fourier method for nonlinear problems on the shortcomings of the 2 3 2 3 de aliasing method the high order accuracy of fourier method makes it the method of choice in many large scale simulations we discuss here the stability of fourier method for nonlinear evolution problems focusing on the two prototypical cases of the inviscid burgers equation and the multi dimensional incompressible euler equations the fourier method for such problems with quadratic nonlinearities comes in two main flavors one is the spectral fourier method the other is the 2 3 2 3 pseudo spectral fourier method where one removes the highest 1 3 1 3 portion of the spectrum this is often the method of choice to maintain the balance of quadratic energy and avoid aliasing errors two main themes are discussed in this paper first we prove that as long as the underlying exact solution has a minimal c 1 alpha c 1 spatial regularity then both the spectral and the 2 3 2 3 pseudo spectral fourier methods are stable consequently we prove their spectral convergence for smooth solutions of the inviscid burgers equation and the incompressible euler equations on the other hand we prove that after a critical time at which the underlying solution lacks sufficient smoothness then both the spectral and the 2 3 2 3 pseudo spectral fourier methods exhibit nonlinear instabilities which are realized through spurious oscillations in particular after shock formation in inviscid burgers equation the total variation of bounded pseudo spectral fourier solutions must increase with the number of increasing modes and we stipulate the analogous situation occurs with the 3d incompressible euler equations the limiting fourier solution is shown to enforce l 2 l 2 energy conservation and the contrast with energy dissipating onsager solutions is reflected through spurious oscillations

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

incompressible euler as a limit of complex fluid models with navier boundary conditions in this article we study the limit 0 of solutions of the euler equations and the limit 0 of solutions of the second grade fluid equations in a bounded domain both in two and in three space dimensions we prove that solutions of the complex fluid models converge to solutions of the incompressible euler equations in a bounded domain with navier boundary conditions under the hypothesis that there exists a uniform time of existence for the approximations independent of and this additional hypothesis is not necessary in 2d where global existence is known and for axisymmetric flows without swirl for which we prove global existence our conclusion is strong convergence in l2 to a solution of the incompressible euler equations assuming smooth initial data

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

decay of almost periodic solutions of conservation laws we consider the asymptotic behavior of solutions of systems of inviscid or viscous conservation laws in one or several space variables which are almost periodic in the space variables in a generalized sense introduced by stepanoff and wiener which extends the original one of h bohr we prove that if u x t is such a solution whose inclusion intervals at time t with respect to 0 satisfy l epsiv t t 0 as t and such that the scaling sequence u t x t u t x t t is pre compact as t in l loc 1 d 1 then u x t decays to its mean value which is independent of t as t the decay considered here is in l 1 loc of the variable x t which implies as we show that as t where m x denotes taking the mean value with respect to x in many cases we show that if the initial data are almost periodic in the generalized sense then so also are the solutions we also show in these cases how to reduce the condition on the growth of the inclusion intervals l t with t as t for fixed 0 to a condition on the growth of l 0 with as 0 which amounts to imposing restrictions only on the initial data we show with a simple example the existence of almost periodic non periodic functions whose inclusion intervals satisfy any prescribed growth condition as 0 the applications given here include inviscid and viscous scalar conservation laws in several space variables some inviscid systems in chromatography and isentropic gas dynamics as well as many viscous 2 2 systems such as those of nonlinear elasticity and eulerian isentropic gas dynamics with artificial viscosity among others in the case of the inviscid scalar equations and chromatography systems the class of initial data for which decay results are proved includes in particular the l generalized limit periodic functions our procedures can be easily adapted to provide similar results for semilinear and kinetic relaxations of systems of conservation laws

convergence of the viscosity method for a nonstrictly hyperbolic conservation law a convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic systemvt vu x 0 u t left frac 1 2 u 2 mathop smallint limits v s s delta r 3 ds right x 0 0 r 3 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

global solutions to the compressible euler equations with geometrical structure we prove the existence of global solutions to the euler equations of compressible isentropic gas dynamics with geometrical structure including transonic nozzle flow and spherically symmetric flow due to the presence of the geometrical source terms the existence results themselves are new especially as they pertain to radial flow in an unbounded region vec x geqq 1 and to transonic nozzle flow arbitrary data withl bounds are allowed in these results a shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions the convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework

cross section and panel data estimators for nonseparable models with endogenous regressors we propose two new methods for estimating models with nonseparable errors and endogenous regressors the first method estimates a local average response one estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning the second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables an external variable is used to impose an equality restriction at two points of support on the conditional distribution of the unobservable random term given the regressor and the external variable our methods apply to cross sections but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group

nonstrictly hyperbolic systems with stiff relaxation terms abstract in this paper a zero factor idea is introduced to extend the convergence framework in g q chen c d levermore t p liu hyperbolic conservation laws with stiff relaxation terms and entropy comm pure appl math 47 1994 787 830 for the singular limits of stiff relaxation from general 2 2 hyperbolic conservation systems to nonstrictly hyperbolic systems and an application of this framework on the so called system of extended traffic flow is obtained

kinetic formulation for systems of two conservation laws and elastodynamics for scalar conservation laws the kinetic formulation makes it possible to generate all the entropies from a simple kernel we show how this concept replaces and simplifies greatly the concept of young measures avoiding the difficulties encountered when working in lp the general construction of the two kinetic functions that generate the entropies of 2 2 strictly hyperbolic systems is also developed here we show that it amounts to building a universal entropy i e one that can be truncated by a kinetic value along riemann invariants for elastodynamics this construction can be completed and specialized using the additional galilean invariance this allows a full characterization of convex entropies it yields a kinetic formulation consisting of two semi kinetic equations which as usual are equivalent to the infinite family of all the entropy inequalities

identification of marginal effects in nonseparable models without monotonicity nonseparable models do not impose any type of additivity between the unobserved part and the observable regressors and are therefore ideal for many economic applications to identify these models using the entire joint distribution of the data as summarized in regression quantiles monotonicity in unobservables has frequently been assumed this paper establishes that in the absence of monotonicity the quantiles identify local average structural derivatives of nonseparable models

global solutions to one dimensional shallow water magnetohydrodynamic equations abstract in this paper we study the cauchy problem for the one dimensional shallow water magnetohydrodynamic equations the main difficulty is the case of zero depth h 0 since the nonlinear flux function p h is singular and the definition of solution is not clear near h 0 first assuming that h has a positive and lower bound we establish the pointwise convergence of the viscosity solutions by using the div curl lemma from the compensated compactness theory to special pairs of functions c f e and obtain a global weak entropy solution second under some technical conditions on the initial data such that the riemann invariants w z are monotonic and increasing we introduce a variant of the vanishing artificial viscosity to select a weak solution finally we extend the results to two special cases where p h is for the polytropic gas or for the chaplygin gas

existence of solutions to hyperbolic conservation laws with a source existence of solutions to three different systems of eqs 1 1 1 2 and 1 3 coming from physically relevant models is shown each needing a different proof which are given in sects 2 3 and 4 the unifying theme is the presence of source terms and the general method of proof is vanishing viscosity together with compensated compactness for system 1 2 entropy entropy flux pairs of lax type are constructed and estimates from singular perturbation theory of odes are used for 1 1 and 1 3 weak entropy entropy flux pairs are constructed following the compensated compactness framework set up by diperna 4

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

initial boundary value problems for conservation laws abstract we establish some general concepts concerning boundary conditions for systems of conservation laws defined on one dimensional space intervals and prove some general results among these is an extension of glimm s existence theorem to initial boundary value problems we also prove the convergence of the time averages of the solutions to certain initial boundary value problems for systems arising in fluid flows in porous media isentropic gas dynamics and elasticity theory

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics