一般区域上在边界退化的拟线性抛物方程的第—初边值问题

对有界域上拟线性抛物方程第一初边值问题，二阶退化拟线性抛物方程初边值问题已有丰富的成果，可见［１］，［２］，［３］，但对任意域上方程的工作则不多见．在此文中，我们讨论任意区域上在边界退化的拟线性抛物方程初边值问题的存在性．     

解线性抛物方程的一类新格式

解线性抛物方程的一类新格式孙志忠（中国科学院计算中心）ＡＮＥＷＣＬＡＳＳＯＦＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＦＯＲＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＳｕｎＺｈｉ－ｚｈｏｎｇ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，Ａ...     

双重退化抛物型方程整体解的存在性和L~∞估计

本文考虑双重退化抛物型方程带有零边界条件的初边值问题的整体解存在性,唯一性和解在模估计．证明了当时,整体解满足估计这里为依赖于ｍ,ｑ,Ｎ和ｒ的适当正常数．     

二阶完全非线性抛物型方程的周期解

证明了二阶完全非线性抛物型方程周期粘性解的存在唯一性，在标准假设下解决了非线性抛物型方程古典周期解的存在唯一性问题。     

伪抛物方程的一些研究进展

本文是关于伪抛物方程的综述,内容包括伪抛物方程的物理背景以及从黏性角度对伪抛物方程的研究,重点介绍半线性伪抛物方程解的渐近行为方面的研究成果,这是目前研究较为深入的领域.     

Limit Behaviors of Solutions for Some Parabolic Equations of Higher Order and Their Applications to the Optimal Control

在本文中，对某些高阶抛物型方程以及某些由抛物型方程所支配的系统的最优控制问题，我们证明了其解的一些极限形态。     

蜕化抛物型方程的Harnack不等式

蜕化抛物型方程的Ｈａｒｎａｃｋ不等式黄清龙（兰州大学数学系，兰州７３００００）提要本文讨论一类蜕化线性抛物型方程，证明其强解具有Ｈａｒｎａｃｋ性质．关键词：抛物型微分方程；蜕化点；Ｈａｒｎａｃｋ性质ＡＭＳ（１９９１）主囹分类：３５Ｋ６５设Ｑ（６，Ｒ）...     

抛物型Bellman方程的周期解和稳定性

抛物型和椭圆型Bellman方程解的存在唯一性结果目前已经比较完善了,[1]中讨论了抛物型Bellman方程的渐近性质。我们在本文中证明抛物型Bellman方程周期解的存在性、唯一性和稳定性。 本文考虑下述抛物型Bellman方程:     

一类非线性伪抛物型方程Cauchy问题的适定性

通过引入算子I-Δ的Bessel势将伪抛物型方程化成抽象的抛物型方程,然后利用算子半群理论讨论了一类非线性伪抛物型方程Cauchy问题的适定性问题.     

具有间断系数的抛物型方程的分段显隐格式

1．在许多实际问题中，热传导是在多种介质中传播的，这些介质的热传导系数有时可以相差好几个量级。六十年代，A．H．和A．A．［1］曾详尽地研究过具有间断系数抛物型方程的差分方法。他们的结果较全面地总结在专著［2］中，关于这方面的文献目录可在该书中找到。众所周知，由于显式抛物型方程差分格式是条件稳定的，时间步长的选取受到两方面的限制，一是正比于空间步长的平方，另一是与热传导系数成反比，因此一般在解抛物型方程时都采用隐式。实际上采用任何格式时间步长的选择还与对计算结果精确度的要求有关，特别是当抛物型方程与…     

Tracking a reference solution of a control system of phase field equations

We consider the problem of tracking a reference solution of a dynamical system described by a pair of distributed differential equations, the phase field equations. To solve this problem, we propose an algorithm based on Yu.S. Osipov’s theory of dynamic inversion and on N.N. Krasovskii’s extremal shift method developed in the theory of positional differential games.     

Dirichlet problem for elliptic equations with nonlinear first order terms: a comparison result

Summary We deal with the Dirichlet problem for elliptic equations with a nonlinearity involving the gradient of the solution. By symmetrization techniques, we reduce the problem of finding sharp estimates of solutions to an analogous problem for ordinary differential equations.Lavoro svolto nell'ambito del G.N.A.F.A. con parziale contributo del M.P.I.     

On the reconstruction of unknown characteristics of a distributed system using a regularized extremal shift

The problem of a stable dynamical reconstruction of unknown characteristics in a distributed system described by a pair of differential equations is considered. The aim of the paper is to construct a solution algorithm for this problem. The proposed algorithm is based on Yu.S. Osipov’s theory of dynamic inversion and N.N. Krasovskii’s extremal shift method.     

Well-posed constraint-preserving boundary conditions for the AA formulation of Einstein's equations

In this paper, we address the problem of artificial boundary conditions for the symmetric linearized hyperbolic formulation of Einstein's equations introduced in [A.M. Alekseenko, D.N. Arnold, New first-order formulation for the Einstein equations, Phys. Rev. D (3) 68 (6) (2003) 064013, 6 pp.]. We prescribe simple boundary conditions that make the problem well-posed and preserve the constraints.     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

Local estimates of normal second derivatives for solutions of the Dirichlet problem for the prescribed quotient curvature equations

Local estimates from above for second normal derivatives of a solution of the Dirichlet problem for the prescribed quotient curvature equations are established. Bibliography: 11 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 114–126. Translated by N. M. Ivochkina.     

On a differential problem coming from cell biology

Summary An initial and boundary value problem for a system of first order linear partial differential equations is studied. This problem arises in cell biology, when the evolution of a homogeneous cell population is modelled. Some existence, uniqueness and regularity results are proven; an estimate for the growth of the cell population is also obtained.This work was in part supported by the Istituto di Analisi Numerica of the C.N.R. in Pavia (Italy), the G.N.A.F.A. of the C.N.R. (Italy) and the Ministero della Pubblica Istruzione (Italy).     

Abstract Volterra operators

We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations.     

The penalty method for equations of viscoelastic media

In the present paper, we study the global classical solvability of the first initial-boundary value problem for some three-dimensional equations and the convergence of solutions of the equations to the classical solutions of the first initial-boundary value problem for the Navier-Stokes equations as ε→0. Bibliography:35 titles. Dedicated to the memory of V. N. Popov Published inZapiski Nauchnykh Seminarov POMI, Vol. 224, 1995, pp. 267–278. Translated by A. P. Oskolkov.     

一类非线性渗流方程Cauchy问题弱解的存在唯一性

讨论具强非线性源和对流项的一般渗流方程以Ｒ＾Ｎ中某一Ｒａｄｏｎ测度为初始迹的Ｃａｕｃｈｙ问题弱解的存在唯一性。