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1.
The global stability of the steady-state solution to a coupled reaction-diffusion system with time delays is investigated. All factors involved in the system, especially, the permeabilites and diffusion are taken into account, and the relevant results of the papers [1, 2] are thus improved.  相似文献   
2.
As We know, maximum principle is very important for elliptic equations. It often provides us with a simple proof for the uniqueness and continuous dependence of solutions on. boundary values,and constitutes the first step of existence proof. Furthermore, it is also useful for the study of properties of solutions. In recent years, some works on the maximum principles of fourth order elliptic equations  相似文献   
3.
Abstract The global stability of the steady-state solution to a coupledreaction-diffusion system with time delays is investigated. All factors involvedin the system, especially, the permeabilites and diffusion are taken into account,and the relevant results of the papers〔1,2〕 are thus improved.  相似文献   
4.
We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature  相似文献   
5.
The homogeneous Dirichlet problem(1) for quasilinear elliptic system in a bounded domain Ω is investigated in this paper. The existence of generalized solutions in [H01(Ω)]N is obtained by using the contructive Galerkin method. For the case of aijlm=0 when i≠j, it is estatablished that such generalized solutions have bounded [L(Ω)]N norm and possess Holeler continuity. Even in the particular case that fi are independent of Du, our results have improved those of A. V. Lair [Ann. Mat. Pura Appl., 116(1978)], allowing bi1(x,u) and fi(x,u) to have a growth in u arbitrarily close to 1.  相似文献   
6.
如和所作过的,二阶拟线性散度型椭圆方程式的Dirichlet问题之W_(mq)~1(Ω)≡W_m~1(Ω)∩L_q(Ω)(m>1,1≤q<∞)广义解的存在性,在比“自然限制”稍多一点的条件下,可以用Galerkin方法予以证明,即先作Galerkin近似,而后证明Galerkin近似的极限点就是所论边值问题之解。这种方法具有一定的构造性。实际上,如能保证解的唯一性,每个Galerkin近似就是一个近似解。本文表明,这种方法照样可以用于拟线性椭圆方程组和其它边值问题。与文[6]稍有不同,本文是把所论方程组的边值问题纳入一个发展了的单调算子方法之一般框架来处理的。这样做是很自然的,因为单调算子方法自问世以来,一直和解椭圆抛物边值问题紧密联系在一起。这方面的开创  相似文献   
7.
本文研究初值问题 u_t=Δu+g(t)f(u) (t>0),u|_(t=0)=u_0(x)和初边值问题 u_t=Δu+g(t,x)f(u) (t>0,x∈Ω),u|_(t=0)=u|_((?))=0之解的整体存在性。如文献[6]中所作的那样,在非线性项中引进因子g(t)或g(t,x),是为了防止解的爆破或熄灭现象发生。本文的结果表明,文献[6]的两个定理中对f,g和u_0的大部分限制可以取消或者减弱;对g可以只要求它在f大时充分小;在一定条件下,控制初始状态即可避免爆破。  相似文献   
8.
严子谦 《中国科学A辑》1987,30(12):1233-1244
在可控和自然增长条件下,非线性抛物组 u''t-DaAia(x,t,u,Du)= Bi(x,t,u,Du),i=1,…,N,(x,t)∈Q之解。u∈L2(0,T;H1(Ω,RN))∩L(0,T;L2(Ω,RN))(或∩L(Q,RN))的空间导数Dau事实上属于Llocp(Q,RN),p>2;拟线性抛物组 u''t-Dα[Aijαβ(x,t,u)Dβuj+aja(x,t,u)]=Bi(x,t,u,Du),i=1,…,N的每一个解都在一开集 Q1?Q上 Holder连续,且Hn+2-p(Q\Q1)=0;若当j>i时Aijαβ=0,且Bi(x,t,u,p)关于|p|的增长阶小于2,则Q1=Q;若Aijαβ和aia都Holder连续,则Dau也在Q1上 Holdler连续.  相似文献   
9.
某些退缩椭圆方程和障碍问题的弱解的正则性   总被引:2,自引:0,他引:2  
谭忠  严子谦 《东北数学》1993,9(2):143-156
  相似文献   
10.
In this paper,the global existence of solutions to the IVP=Δu+g(t)f(u) (t>0),u|_(t=0)=u_0(x)and the (?)PVPu_t=Δu-g(t,x)f(u)(t>0,x∈Ω),u|_(t-0)=u|_(?)(?)is investigated. As has been done in [6]the (?)duction of factor g(t) or g(t.x) innonlinear term is to prevent(?) occurrance of blowing-up or quenching of solutions.It isshown in this paper that most of the restrictions on f,g and u_0 in the theorems of[6] maybe cancelled or relaxed,that the smallness of g is required only for t large,and thatunder certain conditions controlling initial state can avoid blowing-up.  相似文献   
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