Jordan–Cattaneo waves: Analogues of compressible flow

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive Lotka–Volterra equations, including a Lotka–Volterra–Bass competition model with diffusion. For all cases we show how a Jordan–Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo–Christov poroacoustic model.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

Enthalpy Relaxation Study of Poly(Vinyl Chloride) Films Based on the Time-Temperature Superposition Principle

Abstract

In the enthalpy relaxation of poly(vinyl chloride), a decrease in enthalpy upon the isothermal ageing was measured using the differential scanning calorimetry method as a function of ageing time (t_A) and ageing temperature. The range of the ageing temperature was from 56?°C (T_g ? 25?°C) to 72?°C (T_g ? 9?°C) where T_g denotes the glass transition temperature. The limiting value of the decrease in enthalpy was determined by applying a stretched exponential function to the measured enthalpy data. The relaxation function (?) was derived from the measured enthalpy and the construction of a master curve was tried by shifting the ? ? t_A curves of the respective ageing temperatures horizontally. Although there was no agreement between the shift factors (a_T) and the relaxation times of the ? ? t_A curves, the superposition was successfully constructed and the a_T values obtained for the poly(vinyl chloride) sample were found to be comparable to those reported for viscoelastic experiments over a broad temperature range above and below T_g carried out for different polymers. The origin of the decrease in enthalpy was briefly discussed in terms of the chain dynamics in the isothermal condition.     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Well-posedness for the massive nonlinear wave equation on asymptotically AdS spacetimes

In this paper, we prove some well-posedness theorems for the nonlinear massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed by contraction mapping method and also as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.