Wave propagation in an initially stressed transversely isotropic thermoelastic solid half-space

The governing equations of thermoelasticity of transversely isotropic solid with initial stresses are formulated at uniform temperature. These equations are solved analytically in two-dimensions to show the existence of three plane quasi waves, namely, Quasi-Longitudinal (QL), Thermal (T-mode) and Quasi-Transverse (QT) waves. Reflection from a thermally insulated stress free surface of an initial stressed transversely isotropic thermoelastic solid half-space is studied. A particular model is chosen for the numerical computations of the propagation speeds, attenuation coefficients and reflection coefficients. Effects of initial stress parameter and thermal disturbances are observed on speeds of propagation, attenuation coefficients and reflection coefficients.     

An approximate method via Taylor series for stochastic functional differential equations

The subject of this paper is an analytic approximate method for stochastic functional differential equations whose coefficients are functionals, sufficiently smooth in the sense of Fréchet derivatives. The approximate equations are defined on equidistant partitions of the time interval, and their coefficients are general Taylor expansions of the coefficients of the initial equation. It will be shown that the approximate solutions converge in the Lp-norm and with probability one to the solution of the initial equation, and also that the rate of convergence increases when degrees in Taylor expansions increase, analogously to real analysis.     

Asymptotic solutions of the one-dimensional linearized Korteweg–de Vries equation with localized initial data

The Cauchy problem with localized initial data for the linearized Korteweg–de Vries equation is considered. In the case of constant coefficients, exact solutions for the initial function in the form of the Gaussian exponential are constructed. For a fairly arbitrary localized initial function, an asymptotic (with respect to the small localization parameter) solution is constructed as the combination of the Airy function and its derivative. In the limit as the parameter tends to zero, this solution becomes the exactGreen function for the Cauchy problem. Such an asymptotics is also applicable to the case of a discontinuous initial function. For an equation with variable coefficients, the asymptotic solution in a neighborhood of focal points is expressed using special functions. The leading front of the wave and its asymptotics are constructed.     

Arithmetic Continuation of Regular Roots of Formal Parametric Polynomial Systems

Given a regular system of polynomial equations with power series coefficients, an initial root is continued as a power series. With the ground domain as an arbitrary field, arithmetic alone is used for the root continuation over this field, and computation is quadratic in the number of computed coefficients. If the power series of the coefficients of the polynomial are geometrically bounded, then the coefficients of the power series of the root are also.     

On the initial time behavior of spatial derivatives for solutions of the parabolic Cauchy problem

The continuity of the spatial derivatives for solutions of the parabolic Cauchy problem is established down to the initial time under the assumption that the initial data and coefficients are sufficiently smooth.     

First Order Differential Operators Associated to the Cauchy—Riemann Operator in the Plane

The article deals with initial value problems of type δw/δt = Fw, w(0, ·) = φ where t is the time and F is a linear first order operator acting in the z = x ? iy-plane. In view of the classical Cauchy-Kovalevkaya Theorem, the initial value problem is solvable provided F has holomorphic coefficients and the initial function is holomorphic. On the other hand, the Lewy example [H. Lewy (1957). An example of a smooth linear partial differential equation without solution. Ann. of Math., 66, 155–158.] shows that there are equations of the above form with infinitely differentiable coefficients not having any solutions. The article in hand constructs, conversely, all linear operators F for which the initial value problem with an arbitrary holomorphic initial function is always solvable. In particular, we shall see that there are equations of that type whose coefficients are only continuous.     

On long-time asymptotics of solutions of parabolic equations with increasing leading coefficients

Sharp sufficient conditions on the coefficients of a second-order parabolic equation are examined under which the solution of the corresponding Cauchy problem with a power-law growing initial function stabilizes to zero. An example is presented showing that the found sufficient conditions are sharp. Conditions on the coefficients of a parabolic equation are obtained under which the solution of the Cauchy problem with a bounded initial function stabilizes to zero at a power law rate.     

Small Perturbation of Stochastic Parabolic Equations: A Power Series Analysis

A semi-linear second-order stochastic parabolic equation is considered with coefficients, free terms, and initial condition depending on a parameter. It is shown that under some natural conditions the solution can be written as a power series in the parameter. The equations for the coefficients in the power series expansion are derived and the convergence of the power series is studied. An example from nonlinear filtering of diffusion process is discussed.     

低渗透非均质油藏单相渗流敏感系数

建立了在单相低速非达西渗流条件下反求低渗透油藏参数的敏感系数公式,给出了各类非均质油藏条件下压力关于渗透率和孔隙度的数值计算结果。认识到井底压力对井底附近的渗透率更敏感,启动压力梯度的存在,使生产井附近区域敏感系数变大。观测井敏感系数在两井连线区域受启动压力梯度影响很大。     

Global wellposedness of magnetohydrodynamics system with temperature-dependent viscosity

The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.     

Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise

Existence and uniqueness of the mild solutions for stochastic differential equations for Hilbert valued stochastic processes are discussed, with the multiplicative noise term given by an integral with respect to a general compensated Poisson random measure. Parts of the results allow for coefficients which can depend on the entire past path of the solution process. In the Markov case Yosida approximations are also discussed, as well as continuous dependence on initial data, and coefficients. The case of coefficients that besides the dependence on the solution process have also an additional random dependence is also included in our treatment. All results are proven for processes with values in separable Hilbert spaces. Differentiable dependence on the initial condition is proven by adapting a method of S. Cerrai.     

The Inverse Scattering Transform for the Benjamin-Ono Equation—A Pivot to Multidimensional Problems

The initial value problem associated with the Benjamin-Ono equation is linearized by a suitable extension of the inverse scattering transform. Essential is the formulation and solution of an associated nonlocal Riemann-Hilbert problem in terms of initial scattering data. Solitons are given a definitive spectral characterization. Pure soliton solutions are obtained by solving a linear algebraic system whose coefficients depend linearly on [INLINEEQUATION], [INLINEEQUATION].     

A characterization of the Chebyshev and Fibonacci polynomials

We consider sequences of polynomials of hypergeometric type satisfying a three-term recurrence relation with constant coefficients and general initial conditions. We characterize among these the Chebyshev and Fibonacci polynomials. Furthermore, we show some necessary conditions and links between the coefficients of the recurrence relation and initial conditions, and the coefficients of the hypergeometric type differential equation in order that this is satisfied by a sequence of polynomials.     

Propagation and interaction of asymptotic waves in ideal magnetofluiddynamics

Nonlinear three-wave coupling coefficients are derived by a systematic application of nonlinear high frequency geometric optics to the equations of ideal magnetofluiddynamics. These coefficients concern all the possible interactions between Alfvén waves and the two kinds of magnetoacoustic waves: the fast magnetosonic and the slow ones. The propagation of off-resonance waves is also treated and critical times for two specific initial data are found.     

Existence of global strong solutions for Navier–Stokes equations with external force

We consider the initial boundary value problems (IBVPs) for 1D isentropic compressible Navier–Stokes equations with density-dependent viscosity coefficients and external force. If the initial data is regular, the existence and uniqueness of global strong solution to IBVP are proved in this article.     

A non-linear inverse Lanchester square law problem in estimating the force-dependent attrition coefficients

A non-linear inverse Lanchester square law problem using the Conjugate Gradient Method (CGM) , i.e. the iterative regularization method, is examined in this study to estimate the unknown force-dependent attrition coefficients in a general reinforcement schedules by using the observed temporal force strengths. The numerical simulations are performed to test the validity of the present non-linear inverse algorithm by using different types of attrition coefficients. Results show that the advantages of applying the CGM in the inverse calculations lie in that (i) the initial guesses of the attrition coefficients can be chosen arbitrarily and (ii) the force-dependent attrition coefficients can be estimated in a very short computer time.     

Maximum principle for optimal control problems involving impulse controls with nonsmooth data

This paper is concerned with the stochastic maximum principle for impulse optimal control problems of forward–backward systems, where the coefficients of the forward part are Lipschitz continuous. The domain of the regular controls is not necessarily convex. We establish a Pontryagins maximum principle for this control problem by applying Ekelands variational principle to a sequence of approximated control problems with smooth coefficients of the initial problems.     

Asymptotic Solution of the Weakly Nonlinear Schrödinger Equation with Variable Coefficients

A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier-transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schrödinger equation with variable coefficients, and verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schrödinger equation can be valid only for restricted initial conditions.     

一类A(α)稳定的k阶线性k步法公式

本文给出了一类与Gear方法类似的κ阶线性κ步法隐式公式.作者还求出了公式的分数形式的系数,阶数和局部截断误差主项系数,并验证了2-6步公式都具有A(α)稳定的,计算出了它们的幅角α.最后用对比数值实验验证了公式确实是稳定的,并且适合于求解刚性常微分方程.     

Effects of initial stress on guided waves in orthotropic functionally graded plates

Because of the limitation of the manufacturing technology, initial stress in functionally graded materials (FGM) and structures is inevitable. Based on the theory of “Mechanics of Incremental Deformations”, the guided wave propagation in FGM plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the polynomial series method is discussed through the numerical examples. The effects of the initial stress on the Lamb-like wave and on the SH wave are investigated respectively and the numerical results show they are quite distinct. The effect of the gravity on the wave propagation can be ignored. The effects of the initial stress in the thickness direction are very different from those of the initial stress in the wave propagation direction, both on the dispersion curves and on the displacement and stress distributions.