Initial–Boundary Value Problem for a Three-Dimensional Equation of the Parabolic-Hyperbolic Type

Differential Equations - We study an initial–boundary value problem for an equation of the mixed parabolic-hyperbolic type in a rectangular parallelepiped. A uniqueness criterion is...     

Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrodinger Equation

It is well known that Feynman and Hibbs[1] used path integrals over Brownian paths to derive the standard(nonfractional) Schrodinger equation. Recently, Laskin[5, 6] showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known Schrodinger equation, then the path integral over Lévy trajectories leads to the fractional Schrodinger equation. Laskin[7] showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu[4] studied some physical applications of the fractional Schrodinger equation.     

Initial Boundary Value Problem for A Generalized Nonlinear Telegraph Equation with Nonlinear Damping北大核心CSCD

In this paper, the existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the generalized nonlinear telegraph equation with nonlinear damping © 2022 Chinese Academy of Sciences. All rights reserved.     

The Initial Boundary Value Problem for Symmetric Long Wave Equations with Nonhomogeneous Boundary Value

Ｔｈｅ　Ｉｎｉｔｉａｌ　Ｂｏｕｎｄａｒｙ　Ｖａｌｕｅ　Ｐｒｏｂｌｅｍ　ｆｏｒ　Ｓｙｍｍｅｔｒｉｃ　Ｌｏｎｇ　Ｗａｖｅ　Ｅｑｕａｔｉｏｎｓ　ｗｉｔｈ　Ｎｏｎｈｏｍｏｇｅｎｅｏｕｓ　Ｂｏｕｎｄａｒｙ　ＶａｌｕｅＭｉａｏＣｈｃｎｘｉａ（苗晨霞）（Ｉｎｓｔｉ...     

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.     

On the Initial Value Problem for a Parabolic Monge-Ampere Equation

From the theory of optimal investment in mathematical finance,the following initial valueproblem for a parabolic Monge—Ampere equation was derived in吣=0, (8,Y)∈[0,T)×R,where V=y(s,Y)is the unknown function,r,b,仃are given0,b—r>0,and in a typical case,the function g(y)is given by g(v)=1一e-,ky,constants with r≥0,盯>(2)where A iS a positive constant.The practice meaning of the above parameters and functionscan be found in Chapters 2 and 4 in[1】.From the mathematical point of view,the …     

Initial Boundary Value Problems of the Camassa–Holm Equation

In this paper we study initial boundary value problems of the Camassa–Holm equation on the half line and on a compact interval. Using rigorously the conservation of symmetry, it is possible to convert these boundary value problems into Cauchy problems for the Camassa–Holm equation on the line and on the circle, respectively. Applying thus known results for the latter equations we first obtain the local well-posedness of the initial boundary value problems under consideration. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions for the equation on the half line and on a compact interval, respectively. An interesting result of our analysis shows that the Camassa–Holm equation on a compact interval possesses no nontrivial global classical solutions.     

A Kind of Boundary Element Methods for Boundary Value Problem of Helmholtz Equation

1.Problems for electromagnetic scattering are of significant importance in many areas oftechnology.In this paper we discuss the scattering problem of electromagnetic wave incidentby using boundary element method associated with splines.The problem is modelled by aboundary value problem for the Helmholtz equation     

The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation

The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.     

On Vortex Methods for Initial Boundary Value Problems

ＯｎＶｏｒｔｅｘＭｅｔｈｏｄｓｆｏｒＩｎｉｔｉａｌＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓ￥ＺｈａｎｇＰｉｎｇｗｅｎ（张平文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｉｎｇ，１００８７１）Ａｂｓｔｒ...     

Initial Value Problem for a Generalized Korteweg－de Vries Equation with Singular Integral－Differential Terms

ＩｎｉｔｉａｌＶａｌｕｅＰｒｏｂｌｅｍｆｏｒａＧｅｎｅｒａｌｉｚｅｄＫｏｒｔｅｗｅｇ－ｄｅＶｒｉｅｓＥｑｕａｔｉｏｎｗｉｔｈＳｉｎｇｕｌａｒＩｎｔｅｇｒａｌ－ＤｉｆｆｅｒｅｎｔｉａｌＴｅｒｍｓＺｈａｎｇＬｉｎｇａｉ（张领海）（ＩｎｓｔｉｔｕｔｅｏｆＡ...     

一个分数阶微分方程四点边值问题正解的存在性

本文研究下面的分数阶微分方程四点边值问题Dα0+u(t)+f(t,u(t))=0,0相似文献   

奇异两点边值问题正解的存在性

奇异两点边值问题正解的存在性@王俟禹@高文杰...     

一具有阻尼非线性双曲型方程初边值问题整体解的不存在性

本文证明一具有阻尼非线性双曲型方程初边值问题局部广义解的存在性和唯一性,并给出此问题解爆破的充分条件.     

Positive Solutions of a Class of Singular and Nonsingular Boundary Value Problems

ＰｏｓｉｔｉｖｅＳｏｌｕｔｉｏｎｓｏｆａＣｌａｓｓｏｆＳｉｎｇｕｌａｒａｎｄ　ＮｏｎｓｉｎｇｕｌａｒＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓＷａｎｇＪｕｎｙｕ（王俊禹）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ...     

Double Positive Solutions of Fourth-Order Nonlinear Boundary Value Problems

We study boundary value problems for fourth-order ordinary differential equation of the form by imposing growth conditions on f and using a generalization of the multiple fixed point theorem by Leggett-Williams, we show the existence of at least two positive solutions.     

一类分数阶微分方程多点边值问题解的存在性

本文运用Krasnoselskii和Schauder不动点定理,得到了一类分数阶微分方程多点边值问题解的存在性．     

Boundary Value Problems for Second－Order Singular Differential Equations on Infinite Intervals

ＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓｆｏｒＳｅｃｏｎｄ－ＯｒｄｅｒＳｉｎｇｕｌａｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｏｎＩｎｆｉｎｉｔｅＩｎｔｅｒｖａｌｓＬｉｕＷｅｎｂｉｎ（刘文斌）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｅｍａｔｉｃｓａｎ...