THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN

A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.

Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussi nesq Equations

Based on the theory of stratification, the well-posedness of the init ial and boundary value problems for the system of two-dimensional non-hydrosta ti c Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for s ome representative initial and boundary value problems. Several special cases we re discussed.

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN

A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.

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.

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function, μ is the scaled Rayleigh number, K = 1 and α represents the effects of a heat transfer finite Blot number. The cofficients β, δ and γ do not vanish when the boundary, conditions at top and bottom are not identical (β / 0, δ / 0) or nonBoussinesq effects are taked into account (γ / 0). In this paper, the Knobloch equation with α > 0 is considered, the global existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively.

Asymptotic of the Solutions to the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors

In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.

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.

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.

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.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

About well posed initial boundary value problem for changing time direction equation by solution and its solvability

The equation of this type should be nonlinear with nonlinearity at the dominant part defining type of equation. The prime model such equations is diffuse equation with U t=[φ(U x)] x nonmonotone state function φ. In this article are presented studies several equations of this sort.

Blow-up of the Solutions of the Initial Boundary Value Problem of Camassa-Holm Equation

Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of CamassaHolm equation on half axis is also investigated in this paper. When the initial potential is nonnegative,then the classical solution exists globally; if the derivative of initial data on zero point is nonpositire, then the life span of nonzero solution nmst be finite.

THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.

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.

Asymptotic of the Solutions of the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors (Ⅱ)

The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.

The Singularly Perturbed Nonlinear Nonlocal Initial Boundary Value Problems for Reaction Diffusion Equations

The singularly perturbed nonlinear noniocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. By using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied, and by educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are considered.

Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.

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.

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.