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1.
This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.  相似文献   
2.
利用孤立子方程KdV-mKdV的朗斯基解的形式和结构,我们提出了朗斯基形式展开法,运用这一方法获得了KdV-mKdV方程的丰富的新的复合函数解,并且朗斯基行列式中的元素不满足任何线性偏微分方程组.所得到的复合函数解是使用其它的方法得不到的.  相似文献   
3.
该文研究了以下高阶Yamabe型方程Lm,pu?g|u|^p?2u=λf|u|α?2u在有限图上的非平凡正解的存在性,其中Lm,p是一个2m阶差分算子,它是一种p次(?Δ)^m算子更一般化,α≥p≥2,g>0和f>0是定义在G的所有顶点上的实函数,m≥1是一个整数.  相似文献   
4.
In this paper we consider minimizers of the functionalmin{λ1(Ω)++λk(Ω)+Λ|Ω|,:ΩD open} where DRd is a bounded open set and where 0<λ1(Ω)λk(Ω) are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets Ω have finite perimeter and that their free boundary ΩD is composed of a regular part, which is locally the graph of a C1,α-regular function, and a singular part, which is empty if d<d, discrete if d=d and of Hausdorff dimension at most dd if d>d, for some d{5,6,7}.  相似文献   
5.
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.  相似文献   
6.
We are concerned with qualitative analysis of weak solutions for a class of magnetic Laplace equations with lack of compactness. By variational arguments, we establish related nonexistence, existence and multiplicity results.  相似文献   
7.
We investigate the method of conjugate gradients, exploiting inaccurate matrix‐vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring in the theoretical bounds estimated, leading to a practical algorithm. Numerical experiments suggest that this approach has significant potential, including in the steadily more important context of multiprecision computations.  相似文献   
8.
Xi-zhong Liu 《中国物理 B》2022,31(5):50201-050201
A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.  相似文献   
9.
Intelligent reflecting surfaces (IRSs) are anticipated to provide reconfigurable propagation environment for next generation communication systems. In this paper, we investigate a downlink IRS-aided multi-carrier (MC) non-orthogonal multiple access (NOMA) system, where the IRS is deployed to especially assist the blocked users to establish communication with the base station (BS). To maximize the system sum rate under network quality-of-service (QoS), rate fairness and successive interference cancellation (SIC) constraints, we formulate a problem for joint optimization of IRS elements, sub-channel assignment and power allocation. The formulated problem is mixed non-convex. Therefore, a novel three stage algorithm is proposed for the optimization of IRS elements, sub-channel assignment and power allocation. First, the IRS elements are optimized using the bisection method based iterative algorithm. Then, the sub-channel assignment problem is solved using one-to-one stable matching algorithm. Finally, the power allocation problem is solved under the given sub-channel and optimal number of IRS elements using Lagrangian dual-decomposition method based on Lagrangian multipliers. Moreover, in an effort to demonstrate the low-complexity of the proposed resource allocation scheme, we provide the complexity analysis of the proposed algorithms. The simulated results illustrate the various factors that impact the optimal number of IRS elements and the superiority of the proposed resource allocation approach in terms of network sum rate and user fairness. Furthermore, we analyze the proposed approach against a new performance metric called computational efficiency (CE).  相似文献   
10.
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