On the Use of the Initial Values of Recursions

In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth prineiple" of initial values of a recursion.

Global Solutions for a Strongly-coupled Parabolic System with Initial Boundary Values

In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.

EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

The Weak Solutions to Initial Boundary Value Problem for Boltzmann-Poisson System

In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.

Global Weak Solutions of Initial Boundary Value Problem for Boltzmann-Poisson System with Absorbing Boundary

This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.

Blow-up of Solution for a Nonlinear Hyperbolic Equation

In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.

Numerical solutions of second order initial value problems of Bratu-type via optimal homotopy asymptotic method

We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.

Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.

Blow-up of solution for a generalized Boussinesq equation

This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.

QUALITATIVE ANALYSISFOR THE SOLUTION OFKURAMOTO-SIVASHINSKY EQUATION

In this paper, two kinds of initial boundary value problems for Kuramoto_Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the generalized global solutions and the classical global solutions for the equation are proved. Morever, the asymptotic behavior of these solutions are considered under some conditions.

Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in R^(N)

In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R N.If the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)<c^(2)A_(1)/2,where A 1 is a positive constant depend on some sufficiently large T^(*),then we can get the non-global existence of the regular solution for the N-dimensional relativistic Euler equations.

Global solution for quantum Zakharov equations

The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

The Existence and Uniqueness of the Solution for Perio dical Boundary Value Problems of 2k th Order Differential Equations with Resonance

In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.

Blow Up for Solutions of Nonlinear Doubly Degenerate Parabolic Equation

This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.

NONEXISTENCE OF GLOBAL SOLUTIONS OF NONLINEAR HYPERBOLIC EQUATION WITH MATERIAL DAMPING

Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.

On the approximate solution of synoptic flow equation with discontinuous boundary conditions

In the present paper we investigate existence and uniqueness generalized solution for initial boundary value problem of synoptic flow equation with discontinuous boundary conditions. We consider Rothe-Galerkin method for given problem and reduce numerical calculations.

Multi-Cuspon Solutions of the Wadati-Konno-Ichikawa Equation by Riemann-Hilbert Problem Method

In this paper, we consider the initial value problem for a complete integrable equation introduced by Wadati-Konno-Ichikawa (WKI). The solution ?is reconstructed in terms of the solution of a ?matrix Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at one non-singularity point, i.e., . Then, the one-cuspon solution, two-cuspon solutions and three-cuspon solution are discussed in detail. Further, the numerical simulations are given to show the dynamic behaviors of these soliton solutions.

Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space

This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.

THE ACCURATE SOLUTION OF THE INITIALVALUE PROBLEM OF THE EQUATION x'(t) + ax(t) + bx(t-т)=0

Consider the RDDE's initial value problemwhere a, b and τ are arbitrary real constants, and τ＞ 0, φ(θ) is a given initial function.In this paper, we find series expansions of the accurate solution of the initial valueproblem (EI).