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101.
This is a subsequent work of our previous one in [25]. Let the nonlinear terms of non-autonomous parabolic problems with singular initial data satisfy subcritical and critical growth conditions. We first establish the existence of uniform attractors in W1,r(Ω), 1<r<N, for the family of processes corresponding to the equations with external forces being translation bounded but not translation compact. Then, we prove the existence of pullback attractors in Lr(Ω) and W1,r(Ω), respectively, for the process corresponding to the equation with the weaker assumption on the external force than previous one. Finally, we investigate the robust of attractors and establish the existence of pullback exponential attractors for the process acting in Lr(Ω) and W1,r(Ω), respectively. 相似文献
102.
103.
We consider a few numerical methods for solving a one-dimensional convection–diffusion singularly perturbed problem. More precisely, we introduce a modified Bakvalov mesh generated using some implicitly defined functions. Properties of this mesh and convergence results for several methods on it are given. Numerical results are presented in support of the theoretical considerations. 相似文献
104.
105.
106.
A multigrid method based on cyclic reduction strategy is proposed to solve huge, nonsymmetric singular linear systems arising from Markovian queueing networks. A simple way to construct the matrix-dependent prolongation and restriction operators is presented in this paper. Numerical results for multiple queues are given to illustrate the efficiency and robustness of our methods. 相似文献
107.
108.
For a general class of finite element spaces based on local polynomial spaces E with Pp⊂E⊂Qp we construct a vertex-edge-cell and point-value oriented interpolation operators that fulfil anisotropic interpolation error estimates.Using these estimates we prove ε-uniform convergence of order p for the Galerkin FEM and the LPSFEM for a singularly perturbed convection-diffusion problem with characteristic boundary layers. 相似文献
109.
Local existence of multiple positive solutions to a singular cantilever beam equation 总被引:2,自引:0,他引:2
Qingliu Yao 《Journal of Mathematical Analysis and Applications》2010,363(1):138-861
By constructing suitable cone and control functions, we prove some local existence theorems of positive solutions for a singular fourth-order two-point boundary value problem. In mechanics, the problem is called cantilever beam equation. Furthermore, we improve a famous method appeared in the studies of singular boundary value problems. The approximation theorem of completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type play important parts in this work. 相似文献
110.
This paper studies the existence of nontrivial solutions for a class of higher-order m-point singular boundary value problems based on the topological degree of a completely continuous field, the first eigenvalue and its corresponding eigenfunction of a special linear operator. The nonlinear term in the boundary value problems is sign-changing and may be unbounded from below. 相似文献