Calculating the sediment flux of the small coastal watersheds:a modification of global equations

Two kinds of regression equations are used to reproduce the sediment flux of the 26 small coastal watersheds in southeastern China.The first kind is the global equations suggested by Milliman and Syvitski(1992),Mulder and Syvitski(1996),Syvitski et al.(2003),and Syvitski and Milliman(2007).The second kind is the modified equations revised by the characteristics of the coastal watersheds,including the drainage area,mean water discharge,and mean sediment discharge.Compared with the observations of the hydrometric stations,the global equations overestimate the sediment flux by 1–2 orders of magnitude.By using the modified equations,the accuracy of the estimated sediment flux is significantly improved,with the relative error in the range of 7%–24%.The reason for the overestimation mainly caused by different parameters’domain and regression coefficients between global rivers and study coastal watersheds.This study demonstrates that modification needs to be considered when using global regression equations to reproduce the sediment flux of the small coastal watersheds in southeastern China.

GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.

GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS

We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu, who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol.

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.

A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRDINGER EQUATION

We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.

Wave equations and reaction-diffusion equations with several nonlinear source terms

The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.

EXISTENCE AND GLOBAL STABILITY OFPOSITIVE PERIODIC SOLUTION IN A LOGISTIC INTEGRODIFFERENTIAL EQUATION WITH FEEDBACK CONTROL

Sufficient conditions are obtained for the existence and global stability of a positive periodic solution in a periodic logistic integrodifferential equation with feedback control by using the technique of coincidence degree and Lyapunov functional.

Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations

In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.

Global Solution for Fully Nonlinear Parabolic Equations in One-Dimensional Space

We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,ux,uxx)+b（x,t,u,ux）,（x,t）∈（-1,1）×(0,T], u（±1,t）=0,u（x,0）=■（x）, where a is strongly nonlinear with respect to uxxand ■ is not necessarily small.We also deal with nonuniform case.

Global Attractors for the Initial Value Problems of Cohn-Hilliard Equations on Compact Manifolds

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION

In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.

Incompressible limit and stability of all-time solutions to 3-D full Navier-Stokes equations for perfect gases

This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.

ASYMPTOTICAL ANALYSIS OF A REACTIONDIFFUSION EQUATIONS D-SIS EPIDEMIC MODEL

By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic reproductive number which determines whether the disease is extinct or not is found. The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. Some results of the ordinary differential equations model are extended to the present partial differential equations model.

An Improved Feasible QP-free Algorithm for Inequality Constrained Optimization

In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.