波浪在缓坡前的反射特性分析

本文根据波浪在岸前的能量方程，理论分析了波浪反射与波能损失的关系，并进一步通过试验验证分析了波浪反射系数在岸前的变化趋势。

Weak solution for a fourth-order nonlinear wave equation

The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.

Study on pile drivability with one dimensional wave propagation theory

Pile drivability is a key problem during the stage of design and construction installation of pile foundations. The solution to the one dimensional wave equation was used to determine the impact force at the top of a concrete pile for a given ram mass, cushion stiffness, and pile impedance. The kinematic equation of pile toe was established and solved based on wave equation theory. The movements of the pile top and pile toe were presented, which clearly showed the dynamic displacement, including rebound and penetration of pile top and toe. A parametric study was made with a full range of practical values of ram weight, cushion stiffness, dropheight, and pile impedance. Suggestions for optimizing the parameters were also presented. Comparisons between the results obtained by the present solution and in-situ measurements indicated the reliability and validity of the method.

Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations

The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.

Mass transfer analysis for microwave hot in-place recycling of asphalt pavements

In order to realize mass transfer analysis for microwave hot in-place recycling of asphalt pavements, a volume element is established including asphalt mixtures, liquid water and vapor. A mass transfer control model is built by the theory of multiphysics, phase transformation and diffusion. The model contains continuity equation, energy conservation equation, movement equation and vapor diffusion equation. To gain the solution of the mass transfer model, the formulas are simplified to one-dimensional differential equations. And then a mathematical model of boundary conditions is established. The mass transfer velocity and dissipative energy are obtained in different moisture contents through simulation of asphalt pavements recycling. The result indicates that when initial moisture content is certain, mass transfer velocity is almost uniform in depth direction at the same heating time and enertrv absorbed by water i,~ descendino with denletion of moisture.

Effects of substituent and solvent on the UV absorption energy of 4,4'-disubstituted stilbenes

Twenty five samples of 4,4'-disubstituted stilbene derivatives were synthesized, and their UV absorption max wavelengths were determined in over 10 kinds of solvents including cyclohexane, ether, chloroform, acetonitrile and ethanol, in which 242 experimental data were recorded. The effects of substituents and solvents on the energy of their UV absorption max wavelengths were discussed. The research results showed: the energy of UV absorption max wavelengths of 4,4'-disubstituted stilbenes was mainly affected by their intramolecular structure (substituent effect) in a given solvent, that is, the energy is dominated by both of excited-state substituent parameter o-~c and polar substituent constant crp. While their energy was dominated by the substituent effect and solvent effect in different kinds of solvents. An equation quantifying the energy of UV absorption max wavelengths of 4,4'-disubstituted stilbenes was developed. In addition, it is found that the n-octanol/water partition coefficient (logP) is more effective than the solvatochromic dye (ET(30)) in scaling the solvent effect. The equation employed the parameter logP has a better correlation and more specific physical meaning. Further, the energies of UV absorption max wavelengths of some reported compounds were predicted by the obtained equation, which are in agreement with their experimental values.

Null Controllability of Some Degenerate Wave Equations

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.

Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.

Higher-Order Rogue Wave Pairs in the Coupled Cubic-Quintic Nonlinear Schr?dinger Equations

We study some novel patterns of rogue wave in the coupled cubic-quintic nonlinear Schr?dinger equations.Utilizing the generalized Darboux transformation, the higher-order rogue wave pairs of the coupled system are generated.Especially, the first-and second-order rogue wave pairs are discussed in detail. It demonstrates that two classical fundamental rogue waves can be emerged from the first-order case and four or six classical fundamental rogue waves from the second-order case. In the second-order rogue wave solution, the distribution structures can be in triangle,quadrilateral and ring shapes by fixing appropriate values of the free parameters. In contrast to single-component systems, there are always more abundant rogue wave structures in multi-component ones. It is shown that the two higher-order nonlinear coefficients ρ_1 and ρ_2 make some skews of the rogue waves.

UNIFORM DECAY RATE FOR THE TRANSMISSION WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

This paper considers the stabilization of the transmission problem of wave equations with variable coefficients. By introducing both boundary feedback control and distribute feedback control near the transmission boundary, the author establishes the uniform energy decay rate for the problem.

Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations

The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem.The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local one.The proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local problem.Especially when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the boundary.For the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.

Analytical Approximate Solution of Schr?dinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary l-State

We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.