the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

boundary layer behavior in the fluid dynamic limit for a nonlinear model boltzmann equation in this paper we study the fluid dynamic limit for the one dimensional broadwell model of the nonlinear boltzmann equation in the presence of boundaries we consider an analogue of maxwell s diffusive and reflective boundary conditions the boundary layers can be classified as either compressive or expansive in terms of the associated characteristic fields we show that both expansive and compressive boundary layers before detachment are nonlinearly stable and that the layer effects are localized so that the fluid dynamic approximation is valid away from the boundary we also show that the same conclusion holds for short time without the structural conditions on the boundary layers a rigorous estimate for the distance between the kinetic solution and the fluid dynamic solution in terms of the mean free path in thel norm is obtained provided that the interior fluid flow is smooth the rate of convergence is optimal

stationary waves for the discrete boltzmann equation in the half space with reflective boundaries the present paper is concerned with stationary solutions for discrete velocity models of the boltzmann equation with reflective boundary condition in the first half space we obtain a sufficient condition that guarantees the existence and the uniqueness of stationary solutions satisfying the reflective boundary condition as well as the spatially asymptotic condition given by a maxwellian state first the sufficient condition is obtained for the linearized system then this result is applied to prove the existence theorem for the nonlinear equation through the contraction mapping principle also it is shown that the stationary solution approaches the asymptotic maxwellian state exponentially as the spatial variable tends to infinity

stationary solutions for the ellipsoidal bgk model in a slab abstract we address the boundary value problem for the ellipsoidal bgk model of the boltzmann equation posed in a bounded interval the existence of a unique mild solution is established under the assumption that the inflow boundary data does not concentrate too much around the zero velocity and the gas is sufficiently rarefied

existence of a stationary wave for the discrete boltzmann equation in the half space we study the existence and the uniqueness of stationary solutions for discrete velocity models of the boltzmann equation in the first half space we obtain a sufficient condition that guarantees the existence and the uniqueness of solutions connecting the given boundary data and the maxwellian state at a spatially asymptotic point first a sufficient condition is obtained for the linearized system then this result as well as the contraction mapping principle is applied to prove the existence theorem for the nonlinear equation also we show that the stationary wave approaches the maxwellian state exponentially at a spatially asymptotic point

asymptotic behavior of one dimensional discrete velocity models in a slab we prove results on the asymptotic behavior of solutions to discrete velocity models of the boltzmann equation in the one dimensional slab 0 x 1 with general stochastic boundary conditions at x 0 and x 1 assuming that there is a constant wall maxwellian m mi compatible with the boundary conditions and under a technical assumption meaning strong thermalization at the boundaries we prove three types of results i if no velocity has x component 0 there are real valued functions 1 t and 2 t such that in a measure theoretic sense fi 0 t 1 t m i fi 1 t 2 t mi as t 1 and 2 are closely related and satisfy functional equations which suggest that 1 t 1 and 2 t 1 as t ii under the additional assumption that there is at least one non trivial collision term containing a product f k f l with k l where k denotes the x component of the velocity associated with f k we show that in a measure theoretic sense 1 t and 2 t converge to 1 as t this entails l1 convergence of the solution to the unique wall maxwellian for this result k l 0 is admissible iii in the absence of any collision terms but under the assumption that there is an irrational quotient i j l k here i l 0 and j k 0 renewal theory entails that the solution converges to the unique wall maxwellian in l

a new contribution to nonlinear stability of a discrete velocity model for a class of discrete velocity models of kinetic theory we prove exponential nonlinear conditional stability of the constant basic state in the slab 0 1

the discrete boltzmann equation with multiple collisions global existence and stability for the initial value problem this paper deals with the analysis of the initial value problem in all space rd d 2 for the discrete boltzmann equation with multiple collisions after a preliminary analysis of the mathematical modeling of the evolution equations global existence and asymptotic behavior are proven using suitable stability criteria some applications verify the analysis for specific models

a discrete velocity stationary wigner equation this paper is concerned with the one dimensional stationary linear wigner equation a kinetic formulation of quantum mechanics specifically we analyze the well posedness of the boundary value problem on a slab of the phase space with given inflow data for a discrete velocity model we find that the problem is uniquely solvable if zero is not a discrete velocity otherwise one obtains a differential algebraic equation of index 2 and hence the inflow data make the system overdetermined

a random discrete velocity model and approximation of the boltzmann equation an approximation procedure for the boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed in a suitable limit the procedure is shown to converge to the time discretized and spatially homogeneous boltzmann equation

l 1 stability of multi dimensional discrete velocity boltzmann equations we study the l 1 stability of multi dimensional discrete velocity boltzmann equations under suitable smallness assumption on initial data we show that bounded mild solutions are l 1 stable for a stability estimate we employ bony s multi dimensional analysis for total interactions over characteristic planes

on unique localization of constrained signals sources conditions for unique localization of radiating sources by passive sensor arrays are presented unlike in previous analyses the case wherein the signals are constrained to certain loci in the complex plane is addressed two types of constraints are considered the first includes the case of constant amplitude signals and the second includes the case of complex exponential signals the conditions specify the maximum number of sources that can be uniquely localized by a general array satisfying some mild geometrical constraints in terms of the number of sensors and the rank of the correlation matrix of the sources this number exceeds substantially the corresponding number for the unconstrained signals case

on resolving 2m 1 narrow band signals with an m sensor uniform linear array the problem of determining the maximum number of narrowband signals whose parameters can be estimated with a linear array of m equally spaced sensors is examined while this number previously has been taken to be m 1 when the signals are mutually uncorrelated it is shown how to estimate directions and amplitudes for as many as 2m 1 signals this over twofold increase is accomplished by retaining snapshot to snapshot phase information usually lost in algorithms based on spatial correlation matrices the approach uses length 2m real signal vectors rather than the usual m complex vectors it is shown that 2m of these real vectors are linearly independent with probability one and thus in the presence of additive white noise the parameters of 2m 1 signals can be estimated an algorithm for determining directions and amplitudes is presented because of the algorithm s computational complexity its application is limited to small m and low time bandwidth products

existence and uniqueness for nonlinear boundary value problems in kinetic theory a boundary value problem for the stationary nonlinear boltzmann equation in a slab has been examined in a weightedl space it has been proved that the problem possesses a unique solution for boundary data small enough the proof is based on the implicit function theorem it has also been shown that for the linearized problem the fredholm alternative applies

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

spectral correlation of modulated signals part i analog modulation the importance of the concept of cyclostationarity in design and analysis of signal detectors synchronizers and extractors in communication systems is briefly discussed and the central role of spectral correlation in the characterization of random processes that are cyclostationary in the wide sense is explained a spectral correlation function that is a generalization of the power spectral density function is described and a corresponding generalization of the wiener khinchine relation and several other fundamental spectral correlation relations also are described explicit formulas for the spectral correlation function for various types of analog modulated signals are derived this includes pulse and carrier amplitude modulation quadrature amplitude carrier modulation and phase and frequency carrier modulation to illustrate the differing spectral correlation characteristics of different modulation types the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane

high resolution schemes for a hierarchical size structured model in this paper we discuss two explicit finite difference schemes namely a first order upwind scheme and a second order high resolution scheme for solving a hierarchical size structured population model with nonlinear growth mortality and reproduction rates we prove stability and convergence for both schemes and provide numerical examples to demonstrate their capability in solving smooth and discontinuous solutions

measure solutions of the steady boltzmann equation in a slab it is shown that the steady boltzmann equation in a slab 0 a has solutionsx x such that the ingoing boundary measures 0 0 and 0 can be prescribed a priori the collision kernel is truncated such that particles with smallx component of the velocity have a reduced collision rate

the broadwell model in a box strong l 1 convergence to equilibrium the global solution of the one dimensional broadwell model in the interval 0 1 with reflecting boundary conditions at 0 and 1 is shown to converge strongly in l 1 0 1 to the constant equilibrium solution

analysis of an efficient integrator for a size structured population model with a dynamical resource in this paper an efficient numerical method for the approximation of a nonlinear size structured population model is presented the nonlinearity of the model is given by dependency on the environment through the consumption of a dynamical resource we analyse the properties of the numerical scheme and optimal second order convergence is derived we report experiments with academical tests to demonstrate numerically the predicted accuracy of the scheme the model is applied to solve a biological problem the dynamics of an ectothermic population the water flea daphnia magna we analyse its long time evolution and describe the asymptotically stable steady states both equilibria and limit cycles

fir zero forcing multiuser detection and code designs for downlink mc cdma this paper focuses on multiuser detection for multicarrier code division multiple access mc cdma systems employing cyclic prefixed cp or zero padded zp transmission techniques for both systems we consider either the classical linear finite impulse response l fir receiving structures or when the transmitted symbols are improper the proposed widely linear fir wl fir ones which process both the received signal and its complex conjugate version with regard to both cp and zp based downlink configurations it is shown that if the number of users does not exceed a given threshold and their codes are appropriately designed l fir and wl fir universal zero forcing zf multiuser detectors can be synthesized which in the absence of noise guarantee perfect symbol recovery for each user regardless of the underlying frequency selective channel in particular some spreading code examples are provided which satisfy the design rules finally numerical simulations are carried out to show that the theoretical considerations developed herein provide useful guidelines for practical mc cdma system designs

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

a general model of size dependent population dynamics with nonlinear growth rate we study a general model of size dependent population dynamics with nonlinear growth rate the existence of a local solution is shown by using schauder s fixed point theorem uniqueness and continuous dependence on initial data are also established under additional conditions

half space problems for the boltzmann equation a survey this paper reviews recent mathematical results on the half space problem for the boltzmann equation the case of a phase transition is discussed in detail

decay theorems for the broadwell equations in this note we establish boundedness and decay theorems for finitely supported solutions to the broadwell equations with four velocity components there is a vast literature on these and similar equations for details see the survey of platkowski illner and the references contained therein the particular variant of them we examine seems new though nonlinear they are homogeneous of degree one

the boltzmann equation global existence for a rare gas in an infinite vacuum solutions of the boltzmann equation are proved to exist globally in time under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough it is also proved as might be expected in this case that the density of the gas at each point in space goes to zero as time goes to infinity

on the cauchy problem for the discrete boltzmann equation with initial values inl1 ℝ we prove a global existence theorem for a discrete velocity model of the boltzmann equation when the initial values i x have finite entropy and for some constant 0 1 x i x el1

a boundary value problem for the two dimensional broadwell model it is shown that a certain boundary value problem for the steady two dimensional broadwell model on a rectangle has a solution the boundary conditions specify the ingoing particle densities on each side of the rectangle

a separability theorem for 2m conjugate symmetric signals impinging on an m element sensor array we show under reasonable assumptions that an m sensor linear conjugate linear lcl processor can separate up to 2m conjugate symmetric signals including the cases in which up to m of the signals each share the same direction of arrival as each of m other signals numerical evaluations illustrate ways in which the performance of the m sensor lcl processor is superior to that of a conventional 2m sensor linear processor when 2m conjugate symmetric signals are received

large time behavior of the broadwell model of a discrete velocity gas with specularly reflective boundary conditions this paper studies the behavior of the one dimensional broadwell model of a discrete three velocity gas on a bounded domain 0 x 1 with specularly reflective boundary condition at x 0 1 for smooth initial data we show that the initial boundary value problem possesses a unique smooth solution which tends as t to a free state consisting of traveling waves f 1e x ct f 2e x ct f 3e x where each f ie is 2 periodic the convergence is in the weak topology of an appropriate orlicz banach state space no smallness assumptions are made on the data

on nonlinear stationary half space problems in discrete kinetic theory we show that every steady discrete velocity model of the boltzmann equation on the real line i d dx fi ci f which satisfies anh theorem and for which all i 0 has solutions on the half line 0 which take prescribed non negativefi o if i 0 and approach a certain manifold of maxwellians asx such solutions give the density distribution in a knudsen boundary layer in the discrete velocity case

large time behavior of discrete velocity boltzmann equations we study the asymptotic behavior of equations representing one dimensional motions in a fictitious gas with a discrete set of velocities the solutions considered have finite mass but arbitrary amplitude with certain assumptions every solution approaches a state in which each component is a traveling wave without interaction the techniques are similar to those in an earlier treatment of the broadwell model 1

loeb solutions of the boltzmann equation existence problems for the boltzmann equation constitute a main area of research within the kinetic theory of gases and transport theory the present paper considers the spatially periodic case with l1 initial data the main result is that the loeb subsolutions obtained in a preceding paper are shown to be true solutions the proof relies on the observation that monotone entropy and finite energy imply loeb integrability of non standard approximate solutions and uses estimates from the proof of the h theorem two aspects of the continuity of the solutions are also considered

boundary value problems for the steady boltzmann equation we discuss steady boundary value problems for the boltzmann equation with inflow and diffusive boundary conditions in one two and three dimensions with suitable truncations of the collision kernel general existence and uniqueness results are obtained if the domain is sufficiently small in one dimension the existence of solutions on general intervals is obtained by abstract fixed point theory

a global existence theorem for the initial boundary value problem for the boltzmann equation when the boundaries are not isothermal we extend the existence theorem recently proved by hamdache for the initial boundary value problem for the nonlinear boltzmann equation in a vessel with isothermal boundaries to more general situations including the case when the boundaries are not isothermal in the latter case a cut off for large speeds is introduced in the collision term of the boltzmann equation

performance analysis of the cyclic music method of direction estimation for cyclostationary signals the cyclic music algorithm exploits the cyclostationarity exhibited by most man made communication signals to perform signal selective estimation of directions of arrival at an array of sensors in the paper the bias and mean squared error of these direction estimates are derived under the assumption that the signals are complex possibly non gaussian and cyclostationary the analytical results are shown to be excellent predictors of empirical results obtained from computer simulation of the cyclic music algorithm and are also compared with the cramer rao bound which in certain cases can be orders of magnitude less than the cramer rao bound for the directions of arrival of stationary signals

study on the efficiency in the numerical integration of size structured population models we describe a procedure which is useful to select an appropriate numerical method in a size structured population model we consider four different numerical methods based on finite difference schemes or characteristics curves integration we compute an analytical approximation in terms of the discretization parameters for the theoretical error principal terms and the computational cost thus we show the efficiency curve that allows to select the best relationship between the discretization parameters for each numerical method finally we obtain the most efficient numerical method for each test

a boundary value problem for discrete velocity models on considere deux problemes aux valeurs limites non lineaires concernant un ecoulement stationnaire a une dimension entre des plaques paralleles