A Generalization of C—semigroup

§ 1.ＴｈｅＧｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐ　Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｌｅｔＸｂｅａＢａｎａｃｈｓｐａｃｅ,ａｎｄＢ(Ｘ)ｔｈｅｓｐａｃｅｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｉｎｔｏＸ .　Ｄｅｆｉｎｉｔｉｏｎ 1 .1　ＳｕｐｐｏｓｅＣｉｓａｂｏｕｎｄｅｄｉｎｊｅｃｔｉｖｅｏｐｅｒａｔｏｒｆｒｏｍＸｉｎｔｏＸ .Ｔｈｅｆａｍｉｌｙｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓ (Ｓ(ｔ) ) ｔ≥ 0 ｉｓａｇｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐｉｆｉｔｈａｓｔｈｅｆｏｌｌｏｗｉｎｇ…     

关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

微分算子环的素理想

本文利用代数的方法与基本结果，对钟家庆关于微分算子理想的结构基于Ｈ．Ｍａａｓｓ的调和齐式分解所得到的结果，在复系数情形给出了一个纯代数的简短证明，在证明中不需要关于微分算子的齐次性假设     

Heisenberg群上不变微分算子的特征值问题

讨论了Ｈｅｉｓｅｎｂｅｒｇ群Ｈｎ上一类不变微分算子Ｐ＝Σ↑ｍ↓ｌ＝０ａｌＬ＾ｌ的离散特征值的存在性。这里ａｌ〉０，ｌ＝０，１，…，ｍ，ｍ≥２。Ｌ为Ｈｎ上的ｓｕｂ－Ｌａｐｌａｃｅ算子。我们通过建立向量场的Ｐｏｉｎｃａｒｅ型不等式，结合Ｆｒｉｅｄｒｉｃｈｓ对欧氏空间上Ｌａｐｌａｃｅ算子的方法，得到了存在性结果。     

微分算子代数的一种不可约Harish-Chandra模的分类

本文首先讨论了微分算子Ｌｉｅ代数的单性，然后确定出了微分算子Ｌｉｅ代数的权重数都是１的所有不可约Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模。     

一类变系数非齐线性微分方程的算子解法

考察非齐项为ｃｏｓｅ~ｘ或ｓｉｎｅ~ｘ的变系数线性方程,利用文［１］的方法,只要线性微分算子ｐ（ｘ,Ｄ）可以分解为一次因子的乘积,都可以求出其通解．     

d维Bernstein算子加Jacobi权的收敛阶

１．引 言 设Ｓ＝Ｓｄ（ｄ＝１,２,…）是 Ｒｄ中的单纯形,即记ｋ＝（ｋ１,ｋ２,……,ｋｄ）∈Ｒｄ,ｋｉ为非负整数, ,则Ｓ上定义的函数ｆ所对应的ｄ维Ｂｅｒｎｓｔｅｉｎ算子定义为其中 Ｐｎ,ｋ（ｘ）＝是 Ｂｅｒｎｓｔｅｉｎ基函数．引进多维Ｊａｃｏｂｉ权函数, 这里 ．定义Ｂｅｒｎｓｔｅｉｎ权函数 表示微分算子． 记 是单位向量,即第ｉ个分量为１,其余ｄ－１个分量为０, ．定义函数ｆ在方向ｅ上的ｒ阶对称差分为Ｃ（Ｓ）中的加权Ｓｏｂｏｌｅｖ空间为其中Ｓ为Ｓ的内部．定义加权Ｋ－泛函及加权光滑模其中 为加权范数． …     

On Local Integrated Cosine Functions

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ＸｉｓａＢａｎａｃｈｓｐａｃｅ,ｅｑｕｉｐｐｅｄｗｉｔｈａｎｏｒｍ· ,Ｂ(Ｘ)ｓｔａｎｄｓｆｏｒｔｈｅＢａｎａｃｈａｌｇｅｂｒａｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎＸ ,Ｂ(Ｘ ,Ｙ)ｆｏｒｔｈｅｓｅｔｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｔｏａｎｏｔｈｅｒＢａｎａｃｈｓｐａｃｅＹ ,ＡｆｏｒａｃｌｏｓｅｄｏｐｅｒａｔｏｒｏｎＸ ,ρ(Ａ)ｆｏｒｔｈｅｒｅｓｏｌｖｅｎｔｓｅｔｏｆＡ ,Ｄ(Ａ)ｆｏｒｔｈ…     

ON THE COEFFICIENTS APPEARING IN THE EXPANSION OF MELNIKOV FUNCTIONS IN HOMOCLINIC BIFURCATIONS

Ｃｏｎｓｉｄｅｒａｐｌａｎａｒｐｅｒｔｕｒｂｅｄｓｙｓｔｅｍｏｆｔｈｅｆｏｒｍｘ＝Ｈｙ＋εｆ（ｘ，ｙ），ｙ＝－Ｈｘ＋εｇ（ｘ，ｙ）（１）ｗｈｅｒｅＨ，ｆ，ｇａｒｅｆｕｎｃｔｉｏｎｓｏｆｃｌａｓＣ∞．Ａｓｕｍｅｆｏｒε＝０（１）ｔｏｈａｖｅａｈｏｍｏｃ...     

解析算子函数的Schwarz引理的一般形式

该文对Ｆａｎ＾「２」和Ｍｉｓｈｒａ＾「３」关于算子情形的Ｓｃｈｗａｒｚ引理作了进一步的延拓，使其结果对于解析算子函数仍然成立。     

一类含Hysteresis微分子算子的反应扩散方程

In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.     

Asymptotic Behaviour for a Phase-Field Model with Hysteresis in One-Dimensional Thermo-Visco-Plasticity

The asymptotic behaviour for t of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators.     

Two Parabolic Equations with Hysteresis

In this paper we discuss the properties of hysteresis phenomena and give some conclusions about two parabolic equations with hysteresis raised by A. Visintin.     

Some bv properties of the preisach hysteresis operator

We discuss mapping and Lipschitz continuity properties of the Preisach model for hysteresis in the spaces BV[0,1] and W^1,1[0,1]     

Models of hysteresis

The concept ofhysteresis operator is introduced. Existence of a solution is proven for a parabolic differential equation containing a hysteresis operator. A collection of references of mathematical papers on hysteresis is also provided.     

Uniqueness theorem for a Cauchy problem with hysteresis

The Cauchy problem for an ordinary differential equation coupled with a hysteresis operator is studied. Under physically reasonable assumptions on the forcing term, uniqueness of solutions is shown without assuming Lipschitz continuity of the hysteresis curves. The result is true for any kind of hysteresis operators with monotone curves of motion.

     

Sufficient tests for the existence and uniqueness of a solution of the cauchy problem for a differential equation with a hysteresis nonlinearity

For a differential equation with a hysteresis nonlinearity of general type, which can be time-varying, we obtain sufficient conditions for the existence and uniqueness of a solution of the Cauchy problem similar to the well-known Cauchy-Picard, Peano, Perron, and Rosenblatt theorems for ordinary differential equations. We consider examples in which a test for the solution uniqueness similar to the Perron-Rosenblatt theorem is applied to specific differential equations with hysteresis nonlinearities of the form of the Prandtl model of a viscoelastic fiber and a time-varying nonlinearity.     

Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations

The paper deals with the long-time behaviour of evolution systems described by ODEs and PDEs with hysteresis operators. The analysis is based on two concepts. The first one is the outward pointing property of the involved hysteresis operators which implies uniform a priori bounds for solutions, the second one is related to the hysteresis modelling itself and consists in introducing a class of thermodynamically consistent generalized Prandtl–Ishlinskii operators as a model for a nonlinear elastoplastic material law. A stability result for solutions in one-dimensional visco-elasto-plasticity is derived as an illustration of the theory.     

Asymptotic behaviour of a quasilinear hyperbolic equation with hysteresis

The paper deals with the asymptotic behaviour of the solution of a quasilinear hyperbolic equation with hysteresis. A stability result for solution in L¹(Ω) is derived by the nonlinear semigroup approach.