{"title":"Symplectic geometry of the oil displacement Barenblatt equations","authors":"Svetlana S. Mukhina","doi":"10.1016/j.geomphys.2024.105277","DOIUrl":null,"url":null,"abstract":"<div><p>The paper is devoted to the Barenblatt model of oil and water filtration with an admixture of active reagents. This model is used in oil production for hard-to-recover deposits by chemical flooding. The model is described by a system of two first order nonlinear partial differential equations. Conditions for the Buckley–Leverett function, under which the system is reduced to a linear one using symplectic transformations, are found. This makes possible to find classes of exact general solutions of the Barenblatt system and to solve the Cauchy problem.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044024001785","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is devoted to the Barenblatt model of oil and water filtration with an admixture of active reagents. This model is used in oil production for hard-to-recover deposits by chemical flooding. The model is described by a system of two first order nonlinear partial differential equations. Conditions for the Buckley–Leverett function, under which the system is reduced to a linear one using symplectic transformations, are found. This makes possible to find classes of exact general solutions of the Barenblatt system and to solve the Cauchy problem.
期刊介绍：
The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields.
The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered.
The Journal covers the following areas of research:
Methods of:
• Algebraic and Differential Topology
• Algebraic Geometry
• Real and Complex Differential Geometry
• Riemannian Manifolds
• Symplectic Geometry
• Global Analysis, Analysis on Manifolds
• Geometric Theory of Differential Equations
• Geometric Control Theory
• Lie Groups and Lie Algebras
• Supermanifolds and Supergroups
• Discrete Geometry
• Spinors and Twistors
Applications to:
• Strings and Superstrings
• Noncommutative Topology and Geometry
• Quantum Groups
• Geometric Methods in Statistics and Probability
• Geometry Approaches to Thermodynamics
• Classical and Quantum Dynamical Systems
• Classical and Quantum Integrable Systems
• Classical and Quantum Mechanics
• Classical and Quantum Field Theory
• General Relativity
• Quantum Information
• Quantum Gravity
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