l 1 stability estimates for n x n conservation laws let u t f u x 0 be a strictly hyperbolic n times n system of conservation laws each characteristic field being linearly degenerate or genuinely nonlinear in this paper we explicitly define a functional phi phi u v equivalent to the l 1 distance which is almost decreasing i e phi big u t v t big phi big u s v s big leq o ve cdot t s quad hbox for all t s geq 0 for every pair of e approximate solutions u v with small total variation generated by a wave front tracking algorithm the small parameter e here controls the errors in the wave speeds the maximum size of rarefaction fronts and the total strength of all non physical waves in u and in v from the above estimate it follows that front tracking approximations converge to a unique limit solution depending lipschitz continuously on the initial data in the vec l 1 norm this provides a new proof of the existence of the standard riemann semigroup generated by a n n system of conservation laws

hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

robust data fusion for multisensor detection systems minimax robust data fusion schemes for multisensor detection systems with discrete time observations characterized by statistical uncertainty are developed and analyzed block sequential and serial fusion rules are considered the performance measures used and made robust with respect to the uncertainties include the error probabilities of the hypothesis testing problem in the block fusion case and the error probabilities and expected numbers of samples or sensors in the sequential and serial fusion cases for different sensor observation statistics the minimax robust fusion rules are derived for two asymptotic cases of interest when the number of sensors is large and when the number of times the fusion center collects the local sensor decisions is large moreover for the case of identical sensor observation statistics and a large number of sensors it is shown that there is no loss in optimality if local tests using likelihood ratios and equal thresholds are used in the sequential fusion rule in all situations the robust decision rules at the sensors and the fusion center are shown to make use of likelihood ratios and thresholds that depend on the least favorable probability distributions of the uncertainty class describing the statistics of sensor observations

localization effects and measure source terms in numerical schemes for balance laws this paper investigates the behavior of numerical schemes for non linear conservation laws with source terms we concentrate on two significant examples relaxation approximations and genuinely nonhomogeneous scalar laws the main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using riemann based numerical schemes some illustrative and relevant computational results are provided

nonlinear resonance in systems of conservation laws the riemann problem for a general inhomogeneous system of conservation laws is solved in a neighborhood of a state at which one of the nonlinear waves in the problem takes on a zero speed the inhomogeneity is modeled by a linearly degenerate field the solution of the riemann problem determines the nature of wave interactions and thus the riemann problem serves as a canonical form for nonlinear systems of conservation laws generic conditions on the fluxes are stated and it is proved that under these conditions the solution of the riemann problem exists is unique and has a fixed structure this demonstrates that in the above sense resonant inhomogeneous systems generically have the same canonical form the wave curves for these systems are only lipschitz continuous in a neighborhood of the states where the wave speeds coincide and so in contrast to strictly hyperbolic systems the implicit function theorem cannot be applied directly to obtain existence and uniqueness here we show that existence

global bv entropy solutions and uniqueness for hyperbolic systems of balance laws we consider the cauchy problem for n n strictly hyperbolic systems of nonresonant balance laws

suppression of oscillations in godunov s method for a resonant non strictly hyperbolic system we prove the stability of the 2 x 2 godunov numerical method in a resonant nonlinear system of conservation laws the system we study provides one of the simplest settings in which wave speeds can coincide in a nonlinear problem namely an inhomogeneous equation in which the inhomogeneity is treated as an unknown variable ut f a u x o at o this is a model for resonance in more complicated systems such as transonic flow in a variable area duct and certain resonant problems in multiphase flow and elasticity we show that the total variation of the conserved quantities can grow at most linearly in weak solutions generated by the 2 2 godunov method under the assumption that a x satisfies the threshold smoothness condition that the total variation of a x is finite we show by counterexample that the condition is sharp in the sense that there is no bound on the growth rate based on the c norm of this variable this is the most complicated setting in which the stability of the 2 2 godunov method has been demonstrated and our results provide the first such result for a numerical method that is essentially based on the solution of the riemann problem for a resonant non strictly hyperbolic system the solution of the riemann problem is more interesting when wave speeds coincide because the coordinate system of riemann invariants is singular and there exists a multiplicity of possible time asymptotic wave patterns for solutions as a consequence numerical methods that are based on the solution of the riemann problem can introduce spurious oscillations in the approximate solutions indeed counterexamples show that the total variation in u of the waves in the riemann problem step of the 2 x 2 godunov method can tend to infinity as ax 0 even when the initial total variation in u is zero thus our results verify that the averaging step in the godunov method wipes out the numerical oscillations that can occur in the riemann problem solution step of the method we interpret this as demonstrating that numerical methods based on the riemann problem are viable in this non strictly hyperbolic setting

neyman pearson test for zero rate multiterminal hypothesis testing the problem of zero rate multiterminal hypothesis testing is revisited from the perspective of information spectrum approach and finite blocklength analysis a neyman pearson like test is proposed and its non asymptotic performance is clarified for a short block length it is numerically determined that the proposed test is superior to the previously reported hoeffding like test proposed by han kobayashi for a large deviation regime it is shown that our proposed test achieves an optimal trade off between the type i and type ii exponents presented by han kobayashi among the class of symmetric type based testing schemes when the type i error probability is non vanishing the proposed test is optimal up to the second order term of the type ii error exponent the latter term is characterized in terms of the variance of the projected relative entropy density the information geometry method plays an important role in the analysis as well as the construction of the test

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

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

generalized spatio chromatic diffusion a framework for diffusion of color images is presented the method is based on the theory of thermodynamics of irreversible transformations which provides a suitable basis for designing correlations between the different color channels more precisely we derive an equation for color evolution which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space we apply the proposed equation to images represented in several color spaces such as rgb cielab opponent colors and ihs

information measures in scale spaces this article investigates renyi s 1976 generalized entropies under linear and nonlinear scale space evolutions of images scale spaces are useful computer vision concepts for both scale analysis and image restoration we regard images as densities and prove monotony and smoothness properties for the generalized entropies the scale space extended generalized entropies are applied to global scale selection and size estimations finally we introduce an entropy based fingerprint description for textures

stability of a resonant system of conservation laws modeling polymer flow with gravitation abstract we prove l 1 uniqueness and stability for a resonant 2 2 system of conservation laws that arise as a model for two phase polymer flow in porous media the analysis uses the equivalence of the eulerian and lagrangian formulation of this system and the results are first established for an auxiliary scalar equation our methods are based on front tracking approximations for the auxiliary equation and the kru kov entropy condition for scalar conservation laws

choice of measure source terms in interface coupling for a model problem in gas dynamics this paper is devoted to the mathematical and numerical analysis of a coupling procedure for one dimensional euler systems the two systems have different closure laws and are coupled through a thin fixed interface following the work of 5 we propose to couple these systems by a bounded vector valued dirac measure concentrated at the coupling interface which in the applications may have a physical meaning we show that the proposed framework allows to control the coupling conditions and we propose an approximate riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem numerical experiments in constrained optimization problems are then presented to assess the performances of the present method 1 introduction the study of large scale and complex problems exhibiting a wide range of physical space and time scales see for instance 62 35 14 usually requires separate solvers adapted to the resolution of specific scales this is the case of many industrial flows let us quote for example the numerical simulation of two phase flows applied to the burning liquid oxygen hydrogen gas in rocket engines 58 this kind of flow contains both separated and dispersed two phase flows due to atomization and evaporation phenomena this requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled another example concerns turbomachine flows which can be modeled by the euler equations of gas dynamics with different closure laws between the stages of the turbine where the conditions of temperature and pressure are strongly heterogeneous the coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine the method of interface coupling allows to represent the evolution of such flows where different models are separated by fixed interfaces first coupling conditions are specified at the interface to exchange information between the systems the definition of transmission conditions generally results from physical consideration e g the conservation or the continuity of given variables then the transmission conditions are represented at the discrete level the study of interface coupling for nonlinear hyperbolic systems has received attention for several years in 43 the authors study the scalar case from both mathematical and numerical points of view

error exponents for distributed detection of markov sources the paper considers a binary hypothesis testing system in which two sensors simultaneously observe a discrete time finite valued stationary ergodic markov source and transmit m ary messages to a neyman pearson central detector the size m of the message alphabet increases at most subexponentially with the number of observations the asymptotic behavior of the type ii error rate is investigated as the number of observations increases to infinity and the associated error exponent is obtained under mild assumptions on the source distributions this exponent is independent of the test level spl epsiv and the actual codebook sizes m is achieved by a universally optimal sequence of acceptance regions and is characterized by an infimum of informational divergence rate over a class of infinite dimensional distributions important differences due to the observations being markov between the asymptotically optimal distributed tests and their nondistributed counterparts are highlighted the converse results require a blowing up lemma for stationary ergodic markov sources which is also proven

nonlinear resonance for quasilinear hyperbolic equation the purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system for the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source analytical understanding is used to design a numerical scheme based on the random choice method an important physical example is transonic gas flow through a nozzle this analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow including such phenomena as nonlinear stability instability and changing types of waves

solutions a variations bornees pour certains systemes hyperboliques de lois de conservation abstract blake temple trans amer math soc 280 1983 781 795 has described the hyperbolic systems of two conservation laws whose shock and rarefaction curves coincide in this note we prove the global existence of weak solutions for such systems with any bounded variation initial condition the proof is based upon standard numerical schemes as well as upon parabolic regularization the key is that the total variation of the riemann invariants is decreasing in time at least in the case of the initial condition with compact support we prove by using the glimm scheme that the system is decoupling in two conservation laws in one unknown in finite time

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

multiterminal detection with zero rate data compression the asymptotic performance of a multiterminal detection system comprising a central detector and two remote sensors that have access to discrete spatially dependent and temporally memoryless observations is discussed it is assumed that prior to transmitting information to the central detector each sensor compresses its observations at a rate which approaches zero as the sample size tends to infinity and that on the basis of the compressed data from both sensors the central detector seeks to determine whether the true distribution of the observations belongs to a null class ii or an alternative class xi under the criterion that stipulates minimization of the type ii error rate subject to an upper bound epsilon on the type i error rate it is shown that in the case of simple distribution classes mod pi mod mod xi mod 1 the error exponent achievable by such a system has a simple characterization is independent of the value of epsilon and is insensitive to changes in compression rate as long as the asymptotic rate on one of the sensors is zero

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

godunov type approximation for a general resonant balance law with large data abstract we consider the cauchy problem for the 2 2 nonstrictly hyperbolic system a t 0 u t f a u x g a u a x 0 a u t 0 a 0 u 0 for possibly large discontinuous and resonant data the generalized solution to the riemann problem is introduced interaction estimates are carried out using an original change of variables and the convergence of godunov approximations is shown uniqueness is addressed relying on a suitable extension of kru kov s techniques

analysis of a singular hyperbolic system of conservation laws abstract we solve the riemann and cauchy problems globally for a singular system of n hyperbolic conservation laws the system which arises in the study of oil reservoir simulation has only two wave speeds and these coincide on a surface of codimension one in state space the analysis uses the random choice method of glimm comm pure appl math 18 1965 697 715

systems of conservation laws with invariant submanifolds systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation multicomponent chromatogra phy as well as in the study of nonlinear motion in elastic strings here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws this coinci dence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension in the case of 2 x 2 systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide introduction systems of conservation laws which have coinciding shock and rarefaction curves arise in the study of oil reservoir simulation nonlinear wave motion in elastic strings as well as in multicomponent chromatography 1 4 5 6 9 11 12 these systems have many interesting features the riemann problem for these equations can be explicitly solved in the large and wave interactions have a simplified structure even in the presence of a nonconvex flux function for this reason these systems represent some of the few examples for which the cauchy problem has been solved for arbitrary data of bounded variation also hyperbolic degeneracies appear in each of these systems in the present paper we are concerned with characterizing the phenomenon of coinciding shock and rarefaction curves this phenomenon turns out to be a special case of the general phenomenon of a submanifold of r being invariant for weak solutions of a given system of n conservation laws invariant manifolds of higher dimension also appear in physical conservation equations in which the conserved quantities represent concentrations i e when the concentrations c of any of the species vanish the system must reduce to a lower order system that expresses the conservation of the remaining species thus c 0 defines a manifold which is invariant in the sense that solutions that start on the manifold remain there for all time moreover such an invariant manifold of dimension n 1 is the boundary of an dimensional invariant region in the sense of chueh conley and smoller 14 in the case of

a difference scheme for conservation laws with a discontinuous flux the nonconvex case in a previous work by the author convergence was established for a simple difference scheme approximating a scalar conservation law where the flux was concave and had a discontinuous spatially varying coefficient j d towers siam j numer anal 38 2000 pp 681 698 the main result of this paper is an extension of that convergence theorem to the situation where the flux may have any finite number of critical points additionally spatially varying source terms are allowed the spatially varying numerical flux is also shown to satisfy maximum and minimum principles and to be total variation decreasing tvd in time

transient l1 error estimates for well balanced schemes on non resonant scalar balance laws abstract the ability of well balanced wb schemes to capture very accurately steady state regimes of non resonant hyperbolic systems of balance laws has been thoroughly illustrated since its introduction by greenberg and leroux 1996 15 see also the anterior wb glimm scheme in e 1992 8 this paper aims at showing by means of rigorous c t 0 l x 1 estimates that these schemes deliver an increased accuracy in transient regimes too namely after explaining that for the vast majority of non resonant scalar balance laws the c t 0 l x 1 error of conventional fractional step tang and teng 1995 45 numerical approximations grows exponentially in time like exp max g t x as a consequence of the use of gronwall s lemma it is shown that wb schemes involving an exact riemann solver suffer from a much smaller error amplification thanks to strict hyperbolicity their error grows at most only linearly in time see also layton 1984 30 numerical results on several test cases of increasing difficulty including the classical leveque yee s benchmark problem leveque and yee 1990 34 in the non stiff case confirm the analysis

a moving mesh numerical method for hyperbolic conservation laws we show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in l1 r to within o n 2 by a piecewise linear function with o fn nodes the nodes are moved according to the method of characteristics we also show that a previous method of dafermos which uses piecewise constant approxima tions is accurate to o n 1 these numerical methods for conservation laws are the first to have proven convergence rates of greater than o fn 1 2 1 introduction it is well known that the solution of the hyperbolic conservation law

a note on the asymptotics of distributed detection with feedback the effect of feedback on the performance of a distributed neyman pearson detection system consisting of n sensors two stage local quantizers and a global detector is investigated two feedback schemes are discussed only one of which yields an asymptotic gain in performance as measured by an appropriate error exponent

well posedness for a scalar conservation law with singular nonconservative source abstract we consider the cauchy problem for the 2 2 strictly hyperbolic system a t 0 a u 0 a 0 u 0 u t f a u x g a u a x 0 for possibly large discontinuous data the continuous dependence of the solution with respect to both a0 and u0 is shown moreover the solutions are characterized as unique limits of kru kov s entropic solutions constructed with regularized initial data ae0

the decentralized quickest detection problem two detectors making independent observations must decide when a markov chain jumps from state 0 to state 1 the decisions are coupled through a common cost function it is shown that the optimal decision is characterized by thresholds as in the decoupled case however the thresholds are time varying and their computation requires the solution of two coupled sets of dynamic programming equations a comparison to the decoupled case shows the structure of the coupling

stability of conservation laws with discontinuous coefficients we prove l1 contractivity of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable furthermore we show that the l1 difference between solutions to conservation laws with different flux functions is bounded by the total variation with respect to the space variable of the difference between the flux functions

encoding visual information using anisotropic transformations the evolution of information in images undergoing fine to coarse anisotropic transformations is analyzed by using an approach based on the theory of irreversible transformations in particular we show that when an anisotropic diffusion model is used local variation of entropy production over space and scale provides the basis for a general method to extract relevant image features

on the stability functional for conservation laws this note is devoted to the explicit construction of a functional defined on all pairs of l 1 functions with small total variation which is equivalent to the l 1 distance and non increasing along the trajectories of a given system of conservation laws the present definition of this functional does not need any construction of approximate solutions

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

asymptotic optimality of likelihood ratio threshold tests in decentralized detection two distributed systems are considered for discriminating between two finite alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive gaussian noise each system comprises two sensors m ary local quantizers and a fusion center which makes decisions based on quantized source observations the problem of asymptotically optimal quantization is considered in detail for the binary m 2 case it is shown that optimality is achieved by quantizing a locally computed likelihood ratio wherein one distribution is in general different from the appropriate source marginal for the problem of detection in gaussian noise it is further demonstrated that the optimal distributed system attains the same asymptotic performance as the optimal centralized system for appropriate choice of m

convergence of the 2 2 godunov method for a general resonant nonlinear balance law we introduce a generalized solution of the riemann problem for a general resonant nonlinear balance law and we prove the convergence of the 2 x 2 godunov numerical method based on these solutions in particular we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the riemann problem and an interesting multiplicity of time asymptotic wave patterns is observed and characterized

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

the solution of nonstrictly hyperbolic conservation laws may be hard to compute some simple examples of nonstrictly hyperbolic conservation laws are presented that admit certain instability properties with respect to l 1 perturbations of the initial data one of the examples shows that a piecewise constant approximation generates an approximate solution with erroneous qualitative behaviour another example shows that the approximate solution is not well defined for both of these examples a classical stable entropy solution can be given by an explicit formula these properties may cause difficulties for numerical methods based on the solution of riemann problems

analysis and approximation of conservation laws with source terms we consider a conservation law of the form cl i ut f u x ax where a cdot is a bounded piecewise smooth source term and f an even convex function we first characterize the solution to the riemann problem through a new lax type formula then we prove that for a cdot fixed the semigroup associated with cl is an l1 contraction and we obtain an existence theorem for weak solutions to cl we conclude by constructing godunov type difference schemes and proving that these schemes are l infty stable and have stable steady solutions similar in structure to those of cl some numerical tests are reported

unconditionally stable methods for hamilton jacobi equations we present new numerical methods for constructing approximate solutions to the cauchy problem for hamilton jacobi equations of the form ut h dxu 0 the methods are based on dimensional splitting and front tracking for solving the associated non strictly hyperbolic system of conservation laws pt dx h p 0 where p dx u in particular our methods depend heavily on a front tracking method for one dimensional scalar conservation laws with discontinuous coefficients the proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as large time step godunov type or front tracking methods we present several numerical examples illustrating the main features of the proposed methods we also compare our methods with several methods from the literature

a conservation law with point source and discontinuous flux function modelling continuous sedimentation continuous sedimentation of solid particles in a liquid takes place in a clarifier thickener unit which has one feed inlet and two outlets the aim of the paper is to formulate and analyse a dynamic model for this process under idealized physical conditions the conservation of mass yields the scalar conservation law frac partial u x t partial t frac partial partial x f u x t x s t delta x where delta is the dirac measure s is a source and f is a flux function which is discontinuous at three points in the one dimensional space coordinate x under certain regularity assumptions a procedure for constructing a solution locally in time is presented the nonlinear phenomena are complicated and so is the general construction of a solution the problem of nonuniqueness due to the discontinuities of f u cdot is handled by a generalized entropy condition an advantage of this approach is that the a priori boundary conditions at the discontinuities

well posedness for a class of 2 2 conservation laws withl data abstract the cauchy problem for a special class of 2 2 systems of conservation laws with data in l 1 l is considered in the strictly hyperbolic case we prove the existence of a weak solution which depends continuously on the initial data with respect to the l 1 norm this solution can be characterized in terms of a kru kov type entropy condition which is introduced here

on optimal data compression in multiterminal statistical inference the multiterminal theory of statistical inference deals with the problem of estimating or testing the correlation of letters generated from two or many correlated information sources under the restriction of a certain transmission rate for each source a typical example is two binary sources with joint probability p x y where the correlation of x and y is to be tested or estimated given n iid observations xn x1 xn and yn y1 yn only k rn 0 r 1 bits each can be transmitted to a common destination what is the optimal data compression for statistical inference a simple idea is to send the first k letters of xn and yn a simpler problem is the helper case where the optimal data compression of xn is searched for under the condition that all of yn are transmitted it is a long standing problem to determine if there is a better data compression scheme than this simple scheme of sending first k letters the present paper searches for the optimal data compression under the framework of linear threshold encoding and shows that there is a better data compression scheme depending on the value of correlation to this end we evaluate the fisher information in the class of linear threshold compression schemes it is also proved that the simple scheme is optimal when x and y are independent or their correlation is not too large

on the representation of image structures via scale space entropy conditions this paper deals with a novel way for representing and computing image features encapsulated within different regions of scale space employing a thermodynamical model for scale space generation the method derives features as those corresponding to entropy rich image regions where within a given range of spatial scales the entropy gradient remains constant different types of image features defining regions of different information content are accordingly encoded by such regions within different bands of spatial scale

solutions of hamilton jacobi equations and scalar conservation laws with discontinuous space time dependence abstract we establish a unique stable solution to the hamilton jacobi equation u t h k x t u x 0 x t 0 with lipschitz initial condition where k x t is allowed to be discontinuous in the x t plane along a finite number of possibly intersecting curves parameterized by t we assume that for fixed k h k p is convex in p and lim p h k p p the solution is determined by showing that if k is made smooth by convolving k in the x direction with the standard mollifier then the control theory representation of the viscosity solution to the resulting hamilton jacobi equation must converge uniformly as the mollification decreases to a lipschitz continuous solution with an explicit control theory representation this also defines the unique stable solution to the corresponding scalar conservation law u t f k x t u x 0 x t 0 with k discontinuous

a numerical method for first order nonlinear scalar conservation laws in one dimension abstract a numerical method for first order nonlinear scalar hyperbolic conservation laws in one dimension is presented using an idea by dafermos in this paper it is proved that it may be used as a numerical method for a general flux function and a general initial value it is possible to give explicit error estimates for the numerical method the error in the method is far smaller than in any other method the numerical method is illustrated in an example

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity