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 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.

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.

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.

SYMMETRIES, BāCKLUND TRANSFORMATIONS AND BOUNDARY-INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPHY EQUATION

In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.

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.

INITIAL BOUNDARY VALUE PROBLEMS FOR A CLASS OF NONLINEAR INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

This paper studies the global existence of the classical solutions to the following problem:This problem describes the nonlinear vibrations of finite rods with nonlinear vis-coelasticity. Under certain conditions on σand f , we obtained the unique existence of the global classical solution of this problem.

Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method

We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.

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.

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.

Initial Value Problem of Singular n-Laplacian Equation

To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem

In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.

A NONLINEAR TRANSFORMATION AND A BOUNDARY-INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR CONVECTION-DIFFUSION EQUATIONS

With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.

INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION

In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the monotonicity of σi(s) (i= 1,…, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given.

Initial-boundary value problem of one class of nonlinear Schrdinger equations described in molecular crystals

In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.

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.

INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.

The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations

For the more general parabolic Monge-Ampère equations defined by the operator F （D2u ＋ σ（x））, the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equation are established. A new structure condition which is used to get a priori estimate is established.

INITIAL AND BOUNDARY PROBLEMS FOR CERTAIN NONLINEAR DEGENERATR PARABOLIC SYSTEMS

In this paper we are concerned with the following nonlinear degenerate parabolic systems u_t=△x(gradψ(u))+D_xb(u)+f(x.t.u)with Dirichlet boundary conditions,where u,gradψ(u),b and f are vector valued functions and xUnder some structure conditions on the terms of the systems,we have established theresults on existence and uniquence of global solutions of the systems.