Asymptotic Stability of Some Nonlinear Boltzmann-Type Equations

A generalized version of the Tjon-Wu equation is considered. It describes the evolution of the energy distribution in a model of gas in which simultaneous collisions of many particles are permitted. Using the technique of Zolotarev metrics we show that the stationary solution is exponentially stable.     

Moment Equations for Polyatomic Gases

The aim of this paper is to analyze the moment equations for polyatomic gases whose internal degrees of freedom are modeled by a continuous internal energy function. The closure problem is resolved using the maximum entropy principle. The macroscopic equations are divided in two hierarchies—“momentum” and “energy” one. As an example, the system of 14 moments equations is studied. The main new result is determination of the production terms which contain two parameters. They can be adapted to fit the expected values of Prandtl number and/or temperature dependence of the viscosity. The ratios of relaxation times are also discussed.     

Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.     

Generalized Neutrino Equations

I discuss generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten’s method for derivation of arbitrary-spin relativistic equations. Possible physical consequences are discussed.     

Generalized Euler Equations

Zusammenfassung Es sei vorausgesetzt, dass in einem optimalen Steuerprozess die Anzahl der Steuervariabeln s–1 ist, wos die Anzahl der Zustandsvariabeln bedeutet. Es wird gezeigt, dass dann die adjungierten Variabeln eliminiert werden können, so dass ein System von Differentialgleichungen entsteht, das als eine Verallgemeinerung der Eulerschen Gleichungen der Variationsrechnung angesehen werden kann. Dieses Resultat gilt sowohl für diskrete als auch für kontinuierliche Steuersysteme, falls die Steuervariabeln keinen einschränkenden Nebenbedingungen unterworfen werden.     

广义Hammerstein型方程的存在定理

本文利用单调型强制映射满射性和逼近方法建立了广义Ｈａｍｍｅｒｓｔｅｉｎ型方程ｕ＋Ｋ（ｕ）Ｆ（ｕ）＝０解的存在性定理，这里对于实自反Ｂａｎａｃｈ空间Ｘ的共轭空间Ｘ^*的每个ｕ，Ｋ（ｕ）：Ｘ→Ｘ^*是线性映射，Ｆ：Ｘ^*→Ｘ是任一映射．所得结果推广了Ｓｃｈｉｌｉｎｇ，Ｓｒｉｋａｎｔｈ ａｎｄ Ｊｏｓｈｉ等相应的结果     

Generalized Alternating Direction Implicit Method for Projected Generalized Lyapunov Equations

We generalize an alternating direction implicit method for projected generalized Lyapunov equations. Low rank versions of this method is also presented that can be used to compute a low rank approximation of the solution of Lyapunov equations with symmetric, positive semidefinite right‐hand side. Numerical example is given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semigroups for Generalized Birth-and-Death Equations in lp Spaces

We prove the existence of C₀ semigroups related to some birth-and-death type infinite systems of ODEs with possibly unbounded coefficients, in the scale of spaces l^p, For some particular cases we also provide a characterization of the spectra of their generators. For the proof of the generation theorem in the case p > 1 we extend the Chernoff perturbation result ([9]) on relatively bounded perturbations of generators. The results presented here have been used in [5] and they play important role for analysing chaoticity of dynamical systems considered there. As a by-product of our approach we obtain a result related to the classical Shubin theorem [20]. We show that this theorem, saying that for a class of bounded infinite matrices the spectrum of the corresponding maximal operator in l^p is independent on cannot be extended to unbounded matrices.     

Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Regularity Criteria for the Generalized MHD Equations

For Sobolev spaces in Lipschitz domains with no imposed boundary conditions, the Aronszajn–Smith theorem algebraically characterizes coercive formally positive integro-differential quadratic forms. Recently, linear elliptic differential operators with formally positive forms have been constructed with the property that no formally positive forms for these operators can be coercive in any bounded domain. In the present article 4th order operators of this kind are shown by perturbation to have coercive forms that are (necessarily) algebraically indefinite. The perturbation here from noncoercive formally positive forms to coercive algebraically indefinite forms requires Agmon's characterization of coerciveness in smoother domains than Lipschitz.     

Attractor for the Dissipative Generalized Klein-Gordon-Schrodinger Equations

In this paper the authors consider the Cauchy problem of dissipative generalized Klein-Gordon-Schrödinger equations and prove the existence of the maximal attractor in the weak topology sense.     

Generalized Iteration Method for First-Kind Integral Equations

An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K ( x − x '), that decays exponentially. The method relies on deriving via the Wiener–Hopf factorization and solving by suitable iterations in the Fourier complex plane a pair of integral relations, where each iteration accounts for all end point singularities in x of the exact solution. For even and odd kernels, this pair reduces to decoupled, 2nd-kind Fredholm equations, and the iteration yields Neumann series subject to known convergence criteria. This formulation is applied to a classic problem of steady advection-diffusion in the two-dimensional (2D) potential flow of concentrated fluid. The remarkable overlap of recently derived asymptotic expansions for the flux in this case is shown to be intimately related to the analyticity of the kernel Fourier transform.     

Energy Scattering for the Generalized Davey—Stewartson Equations

Abstract Considring the generalized Davey-Stewartson equation i-△u+λ│u│~pu+μE(│u│~q)│u│~(q-2)u=0,where λ>0,μ≥0,E=F~(-1)(ξ_1~2│ξ│~2)F,we obtain the existence of scattering operator in ∑(R~n):u{u∈H~1(R~n):│x│u∈L~2(R~n)}.     

无界区域R1上推广的B-BBM方程的整体吸引子

本文研究了无界区域R^1上推广的B—BBM方程的长时间动力学行为，证明了该方程整体吸引子的存在性．     

广义经典力学中的广义WHITTAKER方程和场方法

本文首先利用能量积分降阶广义经典力学的正则方程并得到广义Whittaker方程.其次,将场方法应用于求广义经典力学方程的积分.最后,举例说明新方程和新方法的应用.     

Flux-Ratio Theorems for Nonlinear Equations of Generalized Diffusion

Flux-ratio theorems compare the flux of matter through partof the boundary of a medium with spatially inhomogeneous transportproperties incorporating diffusion, migration, and temporarytrapping of the transported substance, with the flux measuredin a complementary experiment and usually through a differentpart of the boundary. Any nonlinearity in the transport equationsleads to a breakdown of the Ussing flux-ratio theorem pertainingto all times. A fluxintegral theorem is proved for the casewhen the nonlinearity is in the kinetics of trapping. New resultson the time-lag constants for the asymptotics of the two complementaryfluxes associated with nonlinear trapping show that one canexpect deviations from the results that would hold if Ussing'sgeneral theorem were true for this case. When the nonlinearityis due both to nonlinear trapping kinetics and to concentrationdependence of the diffusion coefficient, a nonlinear flux-integral-ratiotheorem is shown to hold when the substance diffuses (but doesnot migrate) in a spatially homogeneous medium.     

A Generalized Smoother for Linear Ordinary Differential Equations

Ordinary differential equations (ODEs) are equalities involving a function and its derivatives that define the evolution of the function over a prespecified domain. The applications of ODEs range from simulation and prediction to control and diagnosis in diverse fields such as engineering, physics, medicine, and finance. Parameter estimation is often required to calibrate these theoretical models to data. While there are many methods for estimating ODE parameters from partially observed data, they are invariably subject to several problems including high computational cost, complex estimation procedures, biased estimates, and large sampling variance. We propose a method that overcomes these issues and produces estimates of the ODE parameters that have less bias, a smaller sampling variance, and a 10-fold improvement in computational efficiency. The package GenPen containing the Matlab code to perform the methods described in this article is available online.     

Wick型随机广义Burgers方程的确切解

借助白噪声分析、Hermite变换和扩展的双曲函数法,研究了Wick型随机广义Burgers'方程,求出了一些精确的Wick型孤立波解和周期波解.由于Wick型函数难以赋值,为此,我们得到一些特殊情形下的Wick型随机广义Burgers'方程的非Wick型解.     

一般Lyness方程的周期性与严格振动性

研究了一般的Lyness方程 其中a、b∈[0,∞)且a+b>0,初值x_-1、x₀为任意正数。得到了一些新的结果;方程(*)解的周期性的一个必要充分条件;方程(*)的所有解严格振动的充分条件。作为应用,解决了G.Ladas提出的一个公开问题。