Stability criteria for linear second order delay differential system

Consider second order delay differential system where r is a positive constant and all coefficients are real constants.Our main results are as follows:(1) The maximal length of the delay for which the stability of system (*) is maintained is given in the case where the zero solution of system (*) is asymptotically stable in the absence of delay.(2) The necessary and sufficient criteria for judging that asymptetical stability of system (*) is preserved for an arbitrary large delay are obtained.     

PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

This paper studies a kind of non-autonomous respiratory disease model with a lag effect.First of all,the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques.Second,it assumes that all coefficients of the system are periodic.The existence of positive periodic solutions of the system is proven,based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines.In the meantime,the global attract...     

PARAMETER IDENTIFICATION FOR THE DOUBLE POROSITY SYSTEMS IN FRACTURE RESERVOIRS

The inverse parameter problem of the permeable law of the naturally fractured reservoirs with double perosity is of great importance in the exploitation of oil The coefficients in the fluid motion equations are unknown geological parameters. In this paper, the history of matching problem of reservoir systems with double porosity has been discussed from the point of view of the parameter identification of distributed parameter systems, and the problems of identifiability and observability for this system are also dealt with. We have obtained the formulas of Fréchet derivative of the index functional in the identification parameters. These formulas are necessary for calculating identification parameters by a gradient or conjugate gradient method. The conditions of identifiability and observability for the reservoir system with double porosity are given.     

Ground states of a nonlinear Schrdinger system with nonconstant potentials

In the case where either the potentials Vj,μj andβare periodic or Vj are well-shaped andμj andβare anti-well-shaped,existence of a positive ground state of the Schrdinger system -Δu1+V1(x)u1=μ1(x)u31+β(x)u1u22in RN,-Δu2+V2(x)u2=β(x)u21u2+μ2(x)u32in RN,uj∈H1(RN),j=1,2,where N=1,2,3,is proved provided thatβis either small or large in terms of Vj andμj.The system with constant coefficients has been studied extensively in the last ten years,and the nonconstant coefficients case has seldom been studied.It turns out that new technical machineries in the setting of variational methods are needed in dealing with the nonconstant coefficients case.     

Multivalued Stochastic Differential Equations with Non-Lipschitz Coefficients

The existence and uniqueness of solutions to the multivalued stochastic differential equations with non-Lipschitz coefficients are proved, and bicontinuous modifications of the solutions are obtained.     

PERIODIC TRAVELLING-WAVE SOLUTION OF BRUSSELATOR

The Hopf bifurcation Theorem requires that one at first knows all eigenvalues of the linearized system;and a diffieulty in applying the Hopf Theorem is that in the general case we are unable to solve an algebraic equation of degree n (n≥3) with parameter coefficients.This paper firstly proves Theorem 1 which enables us to know the existence of the Hopf bifuecation by direct use of the coefficients of the characteristic equ ation of the linearized system for the case where the characteristic equation of the linearized system has degree 2,3 or 4.Then by using Theorem 1,we gave out the condition for existing a periodic traveling-wave solution of Brusselator in diffusion by Hopf bifurcat on.Finally,we discuss the problem of bifurcation direction and the problem of stability of the bifurcation.     

OSCILLATION AND EXISTENCE OF POSITIVESOLUTIONS OF DIFFERENTIAL EQUATIONSWITH POSITIVE, NEGATIVE COEFFICIENTS

This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The "sharp" conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.     

Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential

We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω R3. The viscosity, heat conduc- tion coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solu- tions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyper- bolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.     

Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations

This paper has made researches on first order neutral differential equations with variable coefficients and several deviations. The asymptotic behavior of nonoscillatory solutions of the equations are discussed. Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained. The relevent results in [1—3] are improved and generalized .     

One-dimensional viscous radiative gas with temperature dependent viscosity

This paper is concerned with the construction of global, large amplitude solutions to the Cauchy problem of the one-dimensional compressible Navier–Stokes system for a viscous radiative gas when the viscosity and heat conductivity coefficients depend on both specific volume and absolute temperature. The data are assumed to be without vacuum,mass concentrations, or vanishing temperatures, and the same is shown to be hold for the global solution constructed. The proof is based on some detailed analysis on uniform positive lower and upper bounds of the specific volume and absolute temperature.     

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.     

ON GREEN＇S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS

We study the Green＇s function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima- Shizuta type of conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves pertaining to different characteristic families. The second result is on the continuous differentiability of the Green＇s function with respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.     

Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.     

THE PROLONGATION STRUCTURES AND NONLOCAL SYMMETRIES FOR MODIFIED BOUSSINESQ SYSTEM

The Wahlquist-Estabrook （WE） prolongation structures of modified Boussi-nesq （MB） system are studied from the coverings point of view. The realizations and classifications of one-dimensional coverings of this system are obtained completely. More-over the sufficient and necessary conditions for a vector field to be a nonlocal symmetry of this system are also demonstrated in the WE prolongation structures.     

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.     

A variational formula for controlled backward stochastic partial differential equations and some application

An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.     

NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

The wave equation with variable coefficients with a nonlinear dissipative boundary feedback is studied. By the Riemannian geometry method and the multiplier technique, it is shown that the closed loop system decays exponentially or asymptotically, and hence the relation between the decay rate of the system energy and the nonlinearity behavior of the feedback function is established.     

A NOTE ON SENSITIVITY ANALYSIS OF SHAPE-FROM-MOMENTS

The shape-from-moments problem is to reconstruct a planar polygon from a set of its complex moments. To reconstruct a polygon means to estimate the vertices and the ordering of the vertices. We notice that some coefficients are very important in finding out the ordering of the vertices. We introduce sensitive factors for the coefficients and use it to analyze sensitivity. These factors are also useful for the sensitivity of the vertices.     

Domain Decomposition Method Modified by Characteristic Finite Element Procedure for System of Parabolic Equations with Discontinuous Coefficients

In this work, system of parabolic equations with discontinuous coefficients is studied. The domain decomposition method modified by a characteristic finite element procedure is applied. A function is defined to approximate the fluxes on inner boundaries by using the solution at the previous level. Thus the parallelism is achieved. Convergence analysis and error estimate are also presented.     

An L 2-theory for a class of SPDEs driven by Lévy processes

In this paper we present an L 2-theory for a class of stochastic partial differential equations driven by Lévy processes.The coefficients of the equations are random functions depending on time and space variables,and no smoothness assumption of the coefficients is assumed.