首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 218 毫秒
1.
关于二阶椭圆方程Dirichlet边值问题混合元的超收敛,在正则矩形网格上,林群和林甲富在文[1]中,采用一阶Raviart-Thomas混合元空间,对有限元解经后处理后,其收敛于精确解的速度从二阶提高到四阶.本文拟将这一结果进行推广,讨论二阶椭圆方程Dirichlet边值问题的k阶Raviart-Thomas混合元的超收敛,得到了以k 3阶速度收敛于精确解的有限元解.  相似文献   

2.
关于猝灭问题的一些结果及其应用   总被引:2,自引:0,他引:2  
戴求亿  顾永耕 《数学学报》2003,46(5):985-992
本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。  相似文献   

3.
Raviart-Thomas混合元的超收敛   总被引:1,自引:0,他引:1  
考虑二阶椭圆方程Dirichlet边值问题在正则矩形网格上k阶RaviartThomas混合有限元的超收敛.对有限元解经插值处理后,与通常的有限元最优误差估计相比,收敛速度提高了两阶.  相似文献   

4.
本文用上下解方法,获得半线性次椭圆方程Dirichlet问题的一些存在性结果.  相似文献   

5.
本文用上下解方法,获得半线性次椭圆方程Dirichlet问题的-些存在性结果.  相似文献   

6.
该文讨论半线性椭圆型方程在环形区域上的Dirichlet(dirchlet-Neumann)边值问题.  相似文献   

7.
高阶半线性椭圆型方程奇摄动广义Dirichlet边值问题   总被引:7,自引:0,他引:7  
莫嘉琪 《数学进展》2006,35(1):75-81
本文讨论了半线性椭圆型方程奇摄动广义边值问题,在适当的条件下研究了Dirichlet边值问题广义解的存在唯一性及其渐近性态。  相似文献   

8.
方程△u+g(|X|)f(u)=0的环上Dirichlet边值问题的多重正对径解   总被引:5,自引:1,他引:4  
考察了二阶半线性椭圆边值问题△u+g(|X|)f(u)=0,R  相似文献   

9.
该文利用锥不动点定理讨论了奇异半正二阶脉冲Dirichlet边值问题正解的存在性.  相似文献   

10.
本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.  相似文献   

11.
For a controlled nonlinear functional-operator equation of the Hammerstein type describing a wide class of controlled initial-boundary value problems, we obtain simple sufficient conditions for the convexity, pointwise boundedness and precompactness of the set of solutions (the reachability tube) in the Lebesgue space. As for boundedness and precompactness, we mean certain conditions of the majorant but not Volterra type requirements which give also the total (with respect to the whole set of admissible controls) preservation of solvability of mentioned equation. As some examples of reduction of a controlled initial-boundary (boundary) value problem to the equation under investigation, and verification of the proposed hypotheses for this equation, we consider the first initial-boundary value problem associated with a semilinear parabolic equation of the second order in a rather general form, and also the Dirichlet problem associated with a semilinear elliptic equation of the second order.  相似文献   

12.
By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first‐ and second‐order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well‐known results for semilinear elliptic equations and the Monge‐Ampère equation. © 2001 John Wiley & Sons, Inc.  相似文献   

13.
一类半线性椭圆型方程正整体解的存在性   总被引:1,自引:1,他引:0  
本文研究了一个半线性椭圆型方程正整体解的存在性问题.利用上下解方法克服了非齐次项出现带来的困难,获得了正整体解存在的必要条件,具体地给出了在此条件下正整体解所处的领域.  相似文献   

14.
Existence, uniqueness and convergence of approximants of positive weak solutions for semilinear second order elliptic inequalities are obtained. The nonlinearities involved in these inequalities satisfy suitable upper or lower bound conditions or monotonicity conditions. The lower bound conditions are allowed to contain the critical Sobolev exponents. The methodology is to establish variational inequality principles for demicontinuous pseudo-contractive maps in Hilbert spaces by considering convergence of approximants and apply them to the corresponding variational inequalities arising from the semilinear second order elliptic inequalities. Examples on the existence, uniqueness and convergence of approximants of positive weak solutions of the semilinear second order elliptic inequalities are given.  相似文献   

15.
In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation. With the help of the Nehari manifold and the center mass function, we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole.  相似文献   

16.
Pinching-估计是研究解的凸性的一种重要方法,主要给出了半线性二阶椭圆偏微分方程的Pinching-估计,并将其推广到一类完全非线性二阶椭圆偏微分方程.  相似文献   

17.
In this paper, we study the effect of domain shape on the multiplicity of positive solutions for the semilinear elliptic equations. We prove a Palais-Smale condition in unbounded domains and assert that the semilinear elliptic equation in unbounded domains has multiple positive solutions.  相似文献   

18.
We consider a semilinear elliptic equation of second order with variable coefficients of the form Lu = e u in the semi-infinite cylinder whose solution satisfies a homogeneous Neumann condition on the lateral surface of the cylinder.  相似文献   

19.
This paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem.  相似文献   

20.
We are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity. We also investigate the non-degeneracy of a positive radial solution for a converted semilinear elliptic equation.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号