一类水污染问题中可扩散界面的适定性研究
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摘要
针对长江水污染问题中污染水层与未污染水层均为受限制含水层的情况,利用Darcy定理和质量守恒定律建立了一个三维耦合抛物线方程组的数学模型;基于偏微分方程的基本理论,采用积分的方式将三维数学模型降成二维数学模型,通过构造截断函数和一个满足一致性假设的算子,利用Schauder定理证明了该二维数学模型解的存在性,从而证明了长江水污染含水层与未污染含水层之间临界面的可行性,为研究长江水污染问题提供了理论依据。
According to the situation that both the polluted layer and the unpolluted layer in the Yangtze River pollution are in confined aquifer,by using Darcy theorem and quality conservation law,the mathematical model of three-dimensional coupled parabolic equation system is set up,based on the basic theory of partial differential equation,by using integral mode,the three dimensional mathematical model is reduced into a two-dimensional model,by constructing truncation function and the operator satisfying consistency conjecture,via using Schauder theorem,the existence of the two-dimensional mathematical model solution is proved,so that the feasibility of critical interface between the polluted water layer and the unpolluted water layer of the Yangtze River pollution problem in the confined aquifer is proved,which provide theoretical basis for studying water pollution problem of the Yangtze River.
According to the situation that both the polluted layer and the unpolluted layer in the Yangtze River pollution are in confined aquifer,by using Darcy theorem and quality conservation law,the mathematical model of three-dimensional coupled parabolic equation system is set up,based on the basic theory of partial differential equation,by using integral mode,the three dimensional mathematical model is reduced into a two-dimensional model,by constructing truncation function and the operator satisfying consistency conjecture,via using Schauder theorem,the existence of the two-dimensional mathematical model solution is proved,so that the feasibility of critical interface between the polluted water layer and the unpolluted water layer of the Yangtze River pollution problem in the confined aquifer is proved,which provide theoretical basis for studying water pollution problem of the Yangtze River.
引文
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[2] BEAR J. Dynamics of Fluids in Porous Media[M].New York:American Elsevier,1972
[3] SHAMIR U,DAGAN G. Motion of the Seawater Interface in Coastal Aquifers:A Numerical Solution[J]. Water Resources Res,1971,7(3):644—657
[4] SIMON J. Compact Sets in the Space Lp(0,T,B)[J].Ann Mat,Pure Appl,1987,146(4):65—96
[5] ZHANG F C,LIAO X F,CHEN Y A,et al. On the Dynamics of the Chaotic General Lorenz System[J].International Journal of Bifurcation and Chaos,2017,27(5):1-7
[6] ZHANG F C,WANG X Y,LIAO X F,et al. Dynamical Behaviors of a Modified Lorenz-Stenflo Chaotic System[J]. International Journal of Bifurcation and Chaos,2017,27(5):1-10
[7] ZHANG F C,LIAO X F,ZHANG G Y. On the Global Boundedness of the LüSystem[J]. Applied Mathematics and Computation,2016,284:332—339
[8] ZHANG F C,CHEN R,WANG X Y,et al. Dynamics of a New 5D Hyperchaotic System of Lorenz Type[J].International Journal of Bifurcation and Chaos,2018,28(3):1-12
[9] ZHANG F C,WANG X Y,XIAO M,et al. On the New Results of Global Exponential Attractive Sets of the T Chaotic System[J]. International Journal of Bifurcation and Chaos,2014,24(7):1-8
[10] XUE Y,XIE J,WU P,et al. A Three-dimensional Miscible Transport Model for Seawater Intrusion in China[J]. Water Resources Res,1995(4):903—1012
[11] Alt H W,LUCKHAU S S. Quasilinear Elliptic-parabolic Differential Equations[J].Math Z,1983(1):311—341