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利用Green函数求解二阶线性非齐次微分方程
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作者 王治国 《高等数学研究》 2025年第4期122-125,共4页
针对二阶线性非齐次微分方程的初值问题,边值问题,半无界问题和全空间问题,介绍了Green函数的求解方法,实例说明了该方法的应用.
关键词 二阶线性微分方程 green函数 STURM-LIOUVILLE问题
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Analysis of problems in urban green space system planning in China 被引量:17
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作者 WANG Xiao-Jun 《Journal of Forestry Research》 SCIE EI CAS CSCD 2009年第1期79-82,共4页
This paper discusses the major problems in urban green space system (UGSS) planning at both general and special planning levels in China. At general planning level, the problems of the UGSS are mainly from the ignor... This paper discusses the major problems in urban green space system (UGSS) planning at both general and special planning levels in China. At general planning level, the problems of the UGSS are mainly from the ignorance in the characteristics of urban nature spaces and the limitation factors of the urban planning system. Great importance is attached to the green spaces in the built area of city, but the green spaces in surrounding areas of the city is unnoticed. Furthermore, because the area of UGSS planning is strictly limited by the administrative zoning, the green space system loses its integrity and rationality in spatial patterns. The schedules of urban development planning mismatched the paces and progresses of the ecological restoration cycles. At special plan level, the problem of the UGSS in China is that the green spaces quantity was over emphasized but the rationality of their layouts is neglected.. Meanwhile, the requirement of the spatial structures and the green spaces layouts to balance between the urban development and the natural ecological environments is often ignored. With regard to the layouts in the UGSS planning practices, the existing problems are the compromising to the existing land-uses, the 'filling in' approach to plan green spaces and an over-emphasis on the layout patterns. 展开更多
关键词 Urban green Space System (UGSS) PLANNING problemS quantity layout
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Problems and Countermeasures of Green Logistics Development in China 被引量:3
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作者 Li Hongxin Qu Qunzhen 《Meteorological and Environmental Research》 CAS 2014年第6期44-46,共3页
Green logistics represents direction and trend of future logistics development, and is a kind of new mode of the logistics industry under the guidance of strategic guidance of scientific development concept and constr... Green logistics represents direction and trend of future logistics development, and is a kind of new mode of the logistics industry under the guidance of strategic guidance of scientific development concept and construction guideline of ecological civilization. Various countries in the world gradually make green logistics activity as the focus of logistics industry development and actively study special technology of green logistics, thereby laying foundation for green and sustainable development of logistics. In China, green logistics starts later, and awareness on green logistics is very limited, We study current situation of green logistics development in China, analyze many problems at concept, regulations and policies, in- frastructure, technical information and logistics personnel of green logistics, and put forward specific suggestions for improving green logistics devel- opment in China. 展开更多
关键词 green logistics Current situation problemS COUNTERMEASURES China
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GRADIENT TYPE OF GREEN'S FUNCTION FOR PARABOLIC PROBLEM
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作者 陈传淼 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1995年第1期85-90,共6页
Consider the piecewise linear finite element subspace S and parabolic semi discrete Green’s function of gradient type G h(t)∈Sk.The asymptotic optimal estimatedxdt【C|Inh| and two applications are discussed.
关键词 PARABOLIC problem green’s FUNCTION GRADIENT TYPE
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A Memetic Algorithm With Competition for the Capacitated Green Vehicle Routing Problem 被引量:9
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作者 Ling Wang Jiawen Lu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第2期516-526,共11页
In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used t... In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor(k NN) based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search(VNS) framework and the simulated annealing(SA) strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station(AFS) adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-ofexperiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP. 展开更多
关键词 Capacitated green VEHICLE ROUTING problem(CGVRP) COMPETITION k-nearest neighbor(kNN) local INTENSIFICATION memetic algorithm
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Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems
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作者 Waleed Al-Hayani 《Applied Mathematics》 2014年第10期1437-1447,共11页
In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions de... In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems. 展开更多
关键词 Adomian Decomposition Method Adomian’s POLYNOMIALS Tenth-Order BOUNDARY Value problems green’s Function
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A Bi-Objective Green Vehicle Routing Problem: A New Hybrid Optimization Algorithm Applied to a Newspaper Distribution
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作者 Júlio César Ferreira Maria Teresinha Arns Steiner 《Journal of Geographic Information System》 2021年第4期410-433,共24页
The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and ... The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and literature Instances, was divided into three stages: Stage 1, data treatment;Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II);Stage 3, analysis of the results, with a comparison of the algorithms. An optimization of 19.9% was achieved for Objective Function 1 (OF<sub>1</sub>;minimization of CO<sub>2</sub> emissions) and consequently the same percentage for the minimization of total distance, and 87.5% for Objective Function 2 (OF<sub>2</sub>;minimization of the difference in demand). Metaheuristic approaches hybrid achieved superior results for case study and instances. In this way, the procedure presented here can bring benefits to society as it considers environmental issues and also balancing work between the routes, ensuring savings and satisfaction for the users. 展开更多
关键词 Bi-Objective green Vehicle Routing problem green Logistics Meta-Heuristic Procedures Case Study Literature Instances
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Solutions of Green's function for Lamb's problem of a two-phase saturated medium 被引量:3
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作者 Boyang Ding,and Jun Chen College of Civil Engineering and Architecture,Zhejiang University of Technology,Hangzhou 310014,China 《Theoretical & Applied Mechanics Letters》 CAS 2011年第5期55-59,共5页
The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of ... The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space. 展开更多
关键词 green's function two-phase saturated medium Lamb's problem
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New Hybrid Algorithm Based on BicriterionAnt for Solving Multiobjective Green Vehicle Routing Problem
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作者 Emile Nawej Kayij Joél Lema Makubikua Justin Dupar Kampempe Busili 《American Journal of Operations Research》 2023年第3期33-52,共20页
The main objective of this paper is to propose a new hybrid algorithm for solving the Bi objective green vehicle routing problem (BGVRP) from the BicriterionAnt metaheuristic. The methodology used is subdivided as fol... The main objective of this paper is to propose a new hybrid algorithm for solving the Bi objective green vehicle routing problem (BGVRP) from the BicriterionAnt metaheuristic. The methodology used is subdivided as follows: first, we introduce data from the GVRP or instances from the literature. Second, we use the first cluster route second technique using the k-means algorithm, then we apply the BicriterionAntAPE (BicriterionAnt Adjacent Pairwise Exchange) algorithm to each cluster obtained. And finally, we make a comparative analysis of the results obtained by the case study as well as instances from the literature with some existing metaheuristics NSGA, SPEA, BicriterionAnt in order to see the performance of the new hybrid algorithm. The results show that the routes which minimize the total distance traveled by the vehicles are different from those which minimize the CO<sub>2</sub> pollution, which can be understood by the fact that the objectives are conflicting. In this study, we also find that the optimal route reduces product CO<sub>2</sub> by almost 7.2% compared to the worst route. 展开更多
关键词 Metaheuristics green Vehicle Routing problem Ant Colony Algorithm Genetic Algorithms green Logistics
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Numerical Solution of Singularly Perturbed Two-Point Boundary Value Problem via Liouville-Green Transform
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作者 Hradyesh Kumar Mishra Sonali Saini 《American Journal of Computational Mathematics》 2013年第1期1-5,共5页
In this paper, authors describe a Liouville-Green transform to solve a singularly perturbed two-point boundary value problem with right end boundary layer in the interval [0, 1]. They reply Liouville-Green transform i... In this paper, authors describe a Liouville-Green transform to solve a singularly perturbed two-point boundary value problem with right end boundary layer in the interval [0, 1]. They reply Liouville-Green transform into original given problem and finds the numerical solution. Then they implemented this method on two linear examples with right end boundary layer which nicely approximate the exact solution. 展开更多
关键词 Singular Perturbation Ordinary Differential Equation BOUNDARY Layer TWO-POINT BOUNDARY Value problem Liouville-green TRANSFORM
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超启发蚁群优化算法求解带柔性时间窗的绿色两级多周期车辆路径问题 被引量:2
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作者 郭宁 钱斌 +3 位作者 申秋义 那靖 胡蓉 耿言 《控制与决策》 北大核心 2025年第3期745-754,共10页
针对带柔性时间窗的绿色两级多周期车辆路径问题(G2E-MPVRPFTW),建立同时以最小化碳排放量和最大化客户满意度为目标的数学模型,提出一种结合K-means带时间窗聚类(KCTW)的超启发蚁群优化算法(HHACOA)进行求解.首先,根据G2E-MPVRPFTW大... 针对带柔性时间窗的绿色两级多周期车辆路径问题(G2E-MPVRPFTW),建立同时以最小化碳排放量和最大化客户满意度为目标的数学模型,提出一种结合K-means带时间窗聚类(KCTW)的超启发蚁群优化算法(HHACOA)进行求解.首先,根据G2E-MPVRPFTW大规模、多约束、强耦合的复杂特性,采用KCTW将该问题分解为多个子问题,以降低问题的求解复杂度;其次,使用HHACOA求解分解后的各子问题,并将这些子问题的解合并获得原问题G2E-MPVRPFTW的解.HHACOA在高层策略域生成9种邻域操作的不同排列,采用蚁群优化算法(ACOA)对优质排列信息进行学习,并基于重构的转移概率矩阵生成新的排列,以有效引导搜索到达优质解集中的区域;HHACOA在低层问题域利用启发式规则和随机方法生成初始种群,并将高层产生的每个排列作为一种算法,作用于种群中的每个个体,以实现在解空间更多不同区域进行搜索. 展开更多
关键词 两级车辆路径问题 多周期 绿色 柔性时间窗 多目标优化 超启发蚁群优化算法
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既有居住建筑节能改造研究综述 被引量:2
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作者 刘舰 刘承宇 《辽宁工业大学学报(自然科学版)》 2025年第1期36-41,共6页
从现状、必要性、现实问题、改造技术4个方面综述了近年来国内关于既有居住建筑改造的研究进展,分析了既有居住建筑节能改造技术研究现状及节能改造推进过程中存在的突出问题,并从政策、资金、规范、管理4个角度提出相应处理建议及解决... 从现状、必要性、现实问题、改造技术4个方面综述了近年来国内关于既有居住建筑改造的研究进展,分析了既有居住建筑节能改造技术研究现状及节能改造推进过程中存在的突出问题,并从政策、资金、规范、管理4个角度提出相应处理建议及解决办法,以期为各地探索本地区既有居住建筑节能改造提供思路与解决方案。 展开更多
关键词 既有建筑 节能改造 能源问题 绿色建筑
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A Study of Optimum Switching Problem for Production Systems Considering Efficiency, Delivery Time and Green Evaluation
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作者 Jing Sun Mingjuan Zhao +1 位作者 Akihiro Yano Hisashi Yamamoto 《Journal of Computer and Communications》 2023年第2期158-171,共14页
This paper aims to derive the optimal switching strategy for production system considering efficiency, delivery time and green evaluation. Nowadays more and more manufacturing and logistics systems not only pursue bet... This paper aims to derive the optimal switching strategy for production system considering efficiency, delivery time and green evaluation. Nowadays more and more manufacturing and logistics systems not only pursue better work efficiency, but also focus on green energy evaluation issues. Cost reduction and shortening of delivery time are always important management issues in pursuit of efficiency and optimization of the entire production system because of global production competition. In a market situation where customer needs change in various ways, in particular, due to inadequate quality, changes in the local environment, natural disasters and so on. Therefore, prompt planning of management measures such as switching work processes and changing production methods has become an important issue. On the other hand, since the Paris Agreement came into effect, the construction of an environment-friendly production system has been required as an approach to environmental problems such as global warming. In this paper, we propose an optimum switching model of production systems considering efficiency, delivery time and green evaluation using a green evaluation index (GEC: Green Energy Coefficient). We also discuss the optimal switching strategy by numerical observation. 展开更多
关键词 green Evaluation Sustainable Production Optimal Switching problem Production Networks Decarbonization Manufacture Management
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value problem Sign-Changing green’s Function Fixed Point Index Iterative Technique Monotone Positive Solution EXISTENCE
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低碳经济背景下考虑需求不确定性的食品冷链物流库存-路径联合优化
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作者 初良勇 林明秀 《上海海事大学学报》 北大核心 2025年第3期85-94,共10页
为降低需求不确定对食品冷链物流的影响,考虑车速、载重等参数,建立油耗测度模型;引入新鲜度衰减函数计算食品配送过程中的货损成本。在此基础上,根据时间窗和零售商服务水平等约束,以包括碳排放成本在内的总成本最低为目标,构建需求不... 为降低需求不确定对食品冷链物流的影响,考虑车速、载重等参数,建立油耗测度模型;引入新鲜度衰减函数计算食品配送过程中的货损成本。在此基础上,根据时间窗和零售商服务水平等约束,以包括碳排放成本在内的总成本最低为目标,构建需求不确定的低碳库存-路径联合优化模型。通过机会约束规划模型进行确定性转化,设计一种基于Tent映射的混沌粒子群优化算法(chaotic particle swarm optimization algorithm based on Tent mapping,TCPSO)对优化模型进行求解。实验结果表明,与单独优化模型相比,联合优化模型的总成本降低了4.95%~9.03%,碳排放成本降低了3.32%~7.59%,物流成本和碳排放量均降低。通过改变车速和需求变异系数,发现总成本随车速增大先降低后上升,随需求波动增大而上升。实例证明所构建的优化模型和设计的算法有效且具有鲁棒性。 展开更多
关键词 绿色库存-路径问题 食品冷链物流 粒子群优化 需求不确定 碳排放
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直角平面区域内固定圆形刚性夹杂问题的Green函数解 被引量:9
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作者 史文谱 刘殿魁 宋永涛 《固体力学学报》 CAS CSCD 北大核心 2006年第2期207-212,共6页
利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足... 利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足直角边界应力自由条件的散射波解,并由叠加原理得到介质内的总波场.最后利用夹杂边界处的位移条件确定出散射波解中的未知系数,最终得到问题的Green函数解,还通过算例讨论了夹杂边界处的径向应力和环向应力随不同波数、角度和不同夹杂位置及不同点源位置的变化情况.算例结果表明了该文方法的有效实用性. 展开更多
关键词 直角平面区域 复变函数法 多极坐标移动技术 反平面问题 green函数解 固定夹杂
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加权Laplace算子Dirichlet特征值问题的一个万有不等式及其应用
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作者 杨贵诚 温杨哲 毛井 《数学物理学报(A辑)》 北大核心 2025年第1期54-73,共20页
该文研究了欧氏空间中具有光滑边界的有界区域Ω上加权Laplace算子L_(φ)的Dirichlet特征值问题.在加权函数φ满足一定约束条件的前提下,利用变分法,并在恰当地构造测试函数的基础上,可以得到该特征值问题的一个万有不等式.
关键词 加权Laplace算子 Dirichlet特征值问题 green公式
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绿肥还田机械研究现状与发展趋势
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作者 刘欣 《农业科技与装备》 2025年第1期61-63,共3页
绿肥还田机械是实施绿肥高效还田技术的重要工具。阐述绿肥还田机械的研究现状,分析常见的几种绿肥还田机械的技术特点与优势,探讨绿肥还田机械存在的主要问题和未来的发展趋势,以期为推动绿肥还田技术的高效应用和农业可持续发展提供... 绿肥还田机械是实施绿肥高效还田技术的重要工具。阐述绿肥还田机械的研究现状,分析常见的几种绿肥还田机械的技术特点与优势,探讨绿肥还田机械存在的主要问题和未来的发展趋势,以期为推动绿肥还田技术的高效应用和农业可持续发展提供参考。 展开更多
关键词 绿肥还田机械 现状 问题 趋势 农业可持续发展
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多点边值问题的Green函数 被引量:3
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作者 葛渭高 《徐州师范大学学报(自然科学版)》 CAS 2008年第2期11-16,共6页
Green函数是研究非线性常微分方程边值问题的重要工具.借助Green函数将微分方程边值问题解的存在性转化成算子不动点的存在性,便于给出边值问题的有解性、多解性以及唯一性的条件.本文给出半齐次线性边值问题Green函数的一般定义,它适... Green函数是研究非线性常微分方程边值问题的重要工具.借助Green函数将微分方程边值问题解的存在性转化成算子不动点的存在性,便于给出边值问题的有解性、多解性以及唯一性的条件.本文给出半齐次线性边值问题Green函数的一般定义,它适用于二阶及高阶方程的两点和多点边值问题,并给出计算方法和若干算例. 展开更多
关键词 微分方程 边值问题 green函数
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关于两相饱和介质中流相Green函数的解析解 被引量:9
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作者 丁伯阳 宋新初 袁金华 《地球物理学报》 SCIE EI CAS CSCD 北大核心 2009年第7期1858-1866,共9页
自然界中许多动力学问题需要用两相饱和介质Green函数求得解答,本文在两相饱和介质位移场Green函数解答的基础上,求得的有关饱和流体孔隙压力,进、排流体流量等三个Green函数.从而使两相饱和介质涉及流体问题的Lamb方程能完整地使用.论... 自然界中许多动力学问题需要用两相饱和介质Green函数求得解答,本文在两相饱和介质位移场Green函数解答的基础上,求得的有关饱和流体孔隙压力,进、排流体流量等三个Green函数.从而使两相饱和介质涉及流体问题的Lamb方程能完整地使用.论文在推导过程中详细地阐述了流体三个Green函数的物理意义,并将所得结果与Chen(1994)的纯数学的结果作了了对比.最后文章讨论了解析解的稳定性. 展开更多
关键词 两相饱和介质 流体问题 green函数
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