Burgers方程与高阶Burgers方程的非线性边-初值问题

本文借助 Cole-Hopf 变换求出了 Burgers 方程在有限区间和半无限直线上非线性边-初值问题的准确解,证明了高阶 Bursers 方程的线性与非线性边-初值问题的解,都可借助相应的线性问题的解来表示,还讨论了非线性边-初值问题解的唯一性.

On the Blowing-up Behaviours for Nonlirear Wave Equations

This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.

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.

Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions

Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation＇s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general botmdary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.

Avoidance of Blow-up by Moving Medium

This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.

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.

On Global Boundedness of Solutions for the Drift-diffusion Semiconductor Equations

This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.

A Class of Two-level High-order Accuracy Explicit Difference Scheme for Solving 3-D Parabolic Partial Differential Equation

A class of two-level high-order accuracy explicit difference scheme for solving 3-D parabolic P.D.E is constructed. Its truncation error is (Δt2+Δx4) and the stability condition is r=Δt/Δx2=Δt/Δy2=Δt/Δz2≤1/6.

On the Asymptotic Property of Solutions to Some Nonlinear Dissipative Wave Equations

In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.

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.

The Migration Equation of the Moisture in Soil with Nonlinear Initial Boundary Value Problem

In this paper,combining Riemann’s method with the fixed point theory effectively,we proved that the migration equation of the moisture in soil with nonlinear initial boundary value problem has unique classical solution.

Asymptotic Behavior of Global Solutions for Double Degenerate Nonlinear Parabolic Equation

In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.

Absorbing Boundary Conditions for Hyperbolic Systems

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

Exponential Attractors for the Ginzburg-Landau-BBM Equations

In this paper, the existence of the exponential attractors for the Ginzburg- Landau-BBM equations with periodic initial and boundary conditions are obtained by using the squeezing property and the operator dccomposition method.

AN INTEGRO-DIFFERENTIAL PARABOLIC VARIATIONAL INEQUALITY ARISING FROM THE VALUATION OF DOUBLE BARRIER AMERICAN OPTION

This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality' solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.

Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics

Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics： Eulerian and La- grangian descriptions of three dimensional （3D） MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clar- ifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global con- straint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-fl limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results field notwithstanding the small resistivity. Strong Faraday in sheet dissipation, resistive heating and topological changes in the induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun＇s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.

Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D

The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)^(-γ)|u(s)|~pds. The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.

Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.

Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum

We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.

NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR THE KORTEWEG-DE VRIES EQUATION ON A BOUNDED DOMAIN

This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H^s(0,1) for any s≥0 via the contraction mapping principle.