半线性抛物型方程组解的整体存在性与爆破速率估计

研究了具有非线性热源的半线性抛物型方程组的齐次neumann问题解的爆破性质.利用上下解方法得到了解整体存在的条件与爆破条件,并利用FriedmannMcleod方法建立了爆破速率估计.     

Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey

We consider nonlinear partial differential equations with several Fuchsian variables of type , where is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variable . The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.

     

Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions

We consider a strongly coupled nonlinear parabolic system which arises in population dynamics in -dimensional domains (). Global existence of classical solutions under certain restrictions on the coefficients is established.

     

Attractors of derivative complex Ginzburg-Landau equation in unbounded domains

The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ² is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in ℝ² is detailed studied.      

A class of Kolmogorov's ecological system with prey having constant adding rate

In this paper, by using the qualitative method, we study a class of Kolmogorov's ecological system with prey having constant adding rate, discuss the relative position and the character of the equilibriums, the global stability of the practical equilibriums and give a group of conditions for the boundedness of the solutions, the nonexistence, the existence and the uniqueness of the limit cycle of the system. Most results obtained in papers [1] and [2] are included or generalized.     

Higher-order Nonlinear System of Equations of Changing Type

In practical problems there appears higher-order equations of changing type([1]). But, there are only a few of papers concerning this type of equations ([2]-[6]). In this paper, the global existence of regular solutions to the Initial-boundary value problem for a class of higher-order system of equations of changing type with a strong nonlinear term is studied.     

非线性力学场论的几个基本课题

最近10年,在变形体转动的描述和应用,应变的度量和应用,以及应力,应变的客观性导数这三个非线性力学场论中互相关联的基本课题方面,提出了许多新问题,作出了大量的研究工作.本文综合介绍了其中一些方面的情况,并概述了笔者的相应工作.      

ASYMPTOTIC ERROR EXPANSION AND DEFECT CORRECTION FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

1.IntroductionLetObearectangulardomain.WeareconcernedwiththeRichardsonextrapolationanddefectcorrectionofthefiniteelementapproximationstothesolutionsofthefollowingsimpleSobolevtypeequationandviscoelasticitytypeequationTheextrapolationtechniqueusedforthefin…     

The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in Hs

In this paper, the local and global existence of solutions for the Cauchy problem of the critical and subcritical nonlinear Schrödinger equations in H^s (s ≥ 2) is studied by using the manner of formal differentiation with respect to time. Some conjectures posed by Cazenave and Weissler in [1] are verified.     

The globalization of Durand-Kerner algorithm

I.Intr0ductionForflndingallzerosofacomplexpolynomialofdegree;Ip(z)=zu olz'-l ..' a.-1z a.(l.l)whenzerosareal1simple,manymethodsareavailable.AmongthemaretheDurand-Kerneralgorithm,theAberthalgorithm,thesquarerootingaIg0rithmandtheirvarietiesI3'[1'141.Thecom…