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1. |
Record Nr. |
UNINA9910864186003321 |
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Autore |
Górny Wojciech |
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Titolo |
Functions of Least Gradient / / by Wojciech Górny, José M. Mazón |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2024 |
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ISBN |
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Edizione |
[1st ed. 2024.] |
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Descrizione fisica |
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1 online resource (442 pages) |
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Collana |
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Monographs in Mathematics, , 2296-4886 ; ; 110 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Mathematical optimization |
Calculus of variations |
Differential equations |
Calculus of Variations and Optimization |
Differential Equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Least Gradient Problem and Minimal Surfaces -- Existence and Characterization of Weak Solutions -- Anisotropic Least Gradient Problem -- Duality Approach -- Existence of Solutions in the Trace Sense -- Uniqueness and Structure of Solutions -- Regularity of Solutions. |
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Sommario/riassunto |
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This book is devoted to the least gradient problem and its variants. The least gradient problem concerns minimization of the total variation of a function with prescribed values on the boundary of a Lipschitz domain. It is the model problem for studying minimization problems involving functionals with linear growth. Functions which solve the least gradient problem for their own boundary data, which arise naturally in the study of minimal surfaces, are called functions of least gradient. The main part of the book is dedicated to presenting the recent advances in this theory. Among others are presented an Euler–Lagrange characterization of least gradient functions, an anisotropic counterpart of the least gradient problem motivated by an inverse problem in medical imaging, and state-of-the-art results concerning existence, regularity, and structure of solutions. Moreover, the authors present a surprising connection between the least gradient problem and the Monge–Kantorovich optimal transport problem and some of its consequences, |
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and discuss formulations of the least gradient problem in the nonlocal and metric settings. Each chapter is followed by a discussion section concerning other research directions, generalizations of presented results, and presentation of some open problems. The book is intended as an introduction to the theory of least gradient functions and a reference tool for a general audience in analysis and PDEs. The readers are assumed to have a basic understanding of functional analysis and partial differential equations. Apart from this, the text is self-contained, and the book ends with five appendices on functions of bounded variation, geometric measure theory, convex analysis, optimal transport, and analysis in metric spaces. |
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2. |
Record Nr. |
UNINA9911004750703321 |
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Autore |
Bourdet Dominique |
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Titolo |
Well test analysis : the use of advanced interpretation models / / Dominique Bourdet |
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Pubbl/distr/stampa |
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Amsterdam ; ; Boston, : Elsevier, 2002 |
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ISBN |
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1-281-07108-0 |
9786611071080 |
0-08-054377-4 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (439 p.) |
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Collana |
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Handbook of petroleum exploration and production, , 1567-8032 ; ; 3 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references ( p. 401-412) and indexes. |
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Nota di contenuto |
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Front Cover; WELL TEST ANALYSIS: THE USE OF ADVANCED INTERPRETATION MODELS; Copyright Page; PREFACE; CONTENTS; CHAPTER 1. PRINCIPLES OF TRANSIENT TESTING; 1.1 Introduction; 1.2 Typical flow regimes; 1.3 Well and reservoir characterization; CHAPTER 2. THE ANALYSIS METHODS; 2.1 Log-log scale; 2.2 Pressure curves analysis; 2.3 Pressure derivative; 2.4 The analysis scales; CHAPTER 3. WELLBORE CONDITIONS; 3.1 Well with wellbore storage and skin; 3.2 Infinite conductivity or uniform flux vertical fracture; 3.3 Finite conductivity vertical fracture; 3.4 Well in partial penetration; 3.5 Slanted |
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well |
3.6 Horizontal well3.7 Skin factors; CHAPTER 4. EFFECT OF RESERVOIR HETEROGENEITIES ON WELL RESPONSES; 4.1 Fissured reservoirs; 4.2 Layered reservoirs with or without crossflow; 4.3 Composite reservoirs; 4.4 Combined reservoir heterogeneities; CHAPTER 5. EFFECT OF RESERVOIR BOUNDARIES ON WELL RESPONSES; 5.1 Single sealing fault in a homogeneous reservoir; 5.2 Two parallel sealing faults in homogeneous reservoir; 5.3 Two intersecting sealing faults in homogeneous reservoir; 5.4 Closed homogeneous reservoir; 5.5 Constant pressure boundary; 5.6 Communicating fault |
5.7 Effect of boundaries in double porosity reservoirs5.8 Effect of boundaries in double permeability reservoirs; 5.9 Effect of boundaries in composite reservoirs; 5.10 Other boundary configurations; 5.11 Conclusion; CHAPTER 6. MULTIPLE WELL TESTING; 6.1 Interference tests in reservoirs with homogeneous behavior; 6.2 Factors complicating interference tests in reservoirs with homogeneous behavior; 6.3 Interference tests in composite reservoirs; 6.4 Interference tests in double porosity reservoirs; 6.5 Interference tests in layered reservoirs; 6.6 Pulse testing; 6.7 Conclusion |
CHAPTER 7. APPLICATION TO GAS RESERVOIRS7.1 Description of gas wells pressure behavior; 7.2 Practical transient analysis of gas well tests; 7.3 Deliverability tests; 7.4 Field example; CHAPTER 8. APPLICATION TO MULIPHASE RESERVOIRS; 8.1 Perrine's method; 8.2 Pseudo-pressure method; 8.3 Pressure squared method; CHAPTER 9. SPECIAL TESTS; 9.1 DST; 9.2 Impulse test; 9.3 Constant pressure test, and rate decline analysis; 9.4 Vertical interference test; CHAPTER 10. PRACTICAL ASPECTS OF WELL TEST INTERPRETATION; 10.1 Factors complicating well test analysis; 10.2 Interpretation procedure |
10.3 Well and reservoir characterisation- interpretation resultsAPPENDIX 1. SUMMARY OF USUAL LOG-LOG RESPONSES; APPENDIX 2. PRACTICAL METRIC SYSTEM OF UNITS; NOMENCLATURE; REFERENCES; AUTHOR INDEX; SUBJECT INDEX |
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Sommario/riassunto |
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This book on well test analysis, and the use of advanced interpretation models is volume 3 in the series Handbook of Petroleum Exploration and Production.The chapters in the book are: Principles of Transient Testing, Analysis Methods, Wellbore Conditions, Effect of Reservoir Heterogeneities on Well Responses, Effect of Reservoir Boundaries on Well Responses, Multiple Well Testing, Application to Gas Reservoirs, Application to Multiphase Reservoirs, Special Tests, Practical Aspects of Well Test Interpretation. |
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