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First-Order Partial Differential Equations, Vol. 2
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Artikel-Nr:
9780486150369
Veröffentl:
2013
Einband:
EPUB
Seiten:
548
Autor:
Hyun-Ku Rhee
Serie:
2, Dover Books on Mathematics
eBook Typ:
EPUB
eBook Format:
Reflowable EPUB
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:
Second volume of a highly regarded 2-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order. Exercises at the end of most chapters, 1989 edition. Includes 198 black-and-white illustrations.
Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order. Examples are drawn from a wide range of scientific and engineering disciplines. The book begins with a consideration of pairs of quasilinear hyperbolic equations of the first order and goes on to explore multicomponent chromatography, complications of counter-current moving-bed adsorbers, the adiabatic adsorption column, and chemical reaction in countercurrent reactors. Exercises appear at the end of most sections. Accessible to anyone with a thorough grounding in undergraduate mathematics — ideally including volume 1 of this set. 1989 edition. 198 black-and-white illustrations. Author and subject indices.
Preface
1. Pairs of Quasilinear Hyperbolic Equations of First-Order
1.1 Equations for the Chromatography of Two Solutes
1.2 Hyperbolic Systems of Two First-Order Equations
1.3 Reducible Equations and Simple Waves
1.4 Characteristic Directions for Two-Solute Chromatography
1.5 Characteristic Initial Value Problem and Riemann Problem
1.6 Compression Waves and the Formation of Shocks
1.7 Discontinuities in Solutions and the Entropy Condition
1.8 Analysis of Polymer Flooding
1.9 Riemann Invariants and Their Application
1.10 Development of Singularities, Weak Solution, and the Entropy Condition
1.11 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions
References
2. Two-Solute chromatography with the Langmuir Isotherm
2.1 Langmuir Isotherm and Characteristic Parameters
2.2 Directions of C-Characteristics and Shock Paths
2.3 Riemann Problems
2.4 The Formation of Shocks
2.5 Fundamentals of Wave Interaction
2.6 Interactions between Waves of the Same Family
2.7 Interactions between Waves of Different Families
2.8 Chromatographic Cycle for Two Solutes
2.9 Introduction to Displacement Development
2.10 Shock Layer Analysis
References
3. Hyperbolic Systems of First-Order Quasilinear Equations and Multicomponent Chromatography
3.1 Equations for the Equilibrium Chromatography of Many Solutes
3.2 Hyperbolic Systems of More than Two First-Order Equations
3.3 Generalized Riemann Invariants and Simple Waves
3.4 Riemann Problem and Fundamental Differential Equations
3.5 Langmuir Isotherm for Multicomponent Adsorption
3.6 Riemann Invariants for Multicomponent Chromatography with the Langmuir Isotherm
3.7 Characteristic Parameters and the space OMEGA(m)
3.8 Characteristic and Simple Waves
3.9 Discontinuities: Shocks
3.10 Entropy Change across a Shock
3.11 Solution of the Riemann Problem
3.12 Illustrations
References
4. Wave Interactions in Multicomponent Chromatography
4.1 Piecewise Constant Data and Patterns of Interaction
4.2 Interactions between Waves of the Same Family
4.3 Interactions between Waves of Different Families
4.4 Chromatographic Cycle for m Solutes
4.5 Multicomponent Separation by Displacement Development
4.6 An Example: Three Solute Separation by Displacement Development
References
5. Multicomponent Adsorption in Continuous Countercurrent Moving-Bed Adsorber
5.1 Basic Formulation
5.2 Theoretical Development for the Langmuir Isotherm
5.3 Analysis of Semi-Infinite Columns
5.4 Analysis of a Finite Column
5.5 Analysis of Wave Interactions
5.6 Illustrations
References
6. More on Hyperbolic Systems of Quasilinear Equations and Analysis of Adiabatic Adsorption Column
6.1 Equations for the Adiabatic Adsorption Column
6.2 Formulation for the Riemann Problem
6.3 Construction of a Continuous Solution
6.4 Discontinuities, Weak Solutions, and the Entropy Condition
6.5 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions
6.6 Solution Scheme for a Moving-Bed Problem
6.7 Adiabatic Adsorption of Single Solute
6.8 Adiabatic Adsorption of Two Solutes
6.9 Adiabatic Adsorption with Adsorptivity Reversal
6.10 Shock Layer Analysis of Adiabatic Adsorption References
7. Chemical Reaction in a countercurrent Reactor
7.1 General Formulation
7.2 Case of Two Reactants
7.3 Characteristics and Discontinuities for the Case of Two Reactants with Adsorption Equilibrium
7.4 The Steady State
7.5 General Procedure for Mapping Out the Steady-State Solution
7.6 Further Developments
References
Author Index; Subject Index
1. Pairs of Quasilinear Hyperbolic Equations of First-Order
1.1 Equations for the Chromatography of Two Solutes
1.2 Hyperbolic Systems of Two First-Order Equations
1.3 Reducible Equations and Simple Waves
1.4 Characteristic Directions for Two-Solute Chromatography
1.5 Characteristic Initial Value Problem and Riemann Problem
1.6 Compression Waves and the Formation of Shocks
1.7 Discontinuities in Solutions and the Entropy Condition
1.8 Analysis of Polymer Flooding
1.9 Riemann Invariants and Their Application
1.10 Development of Singularities, Weak Solution, and the Entropy Condition
1.11 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions
References
2. Two-Solute chromatography with the Langmuir Isotherm
2.1 Langmuir Isotherm and Characteristic Parameters
2.2 Directions of C-Characteristics and Shock Paths
2.3 Riemann Problems
2.4 The Formation of Shocks
2.5 Fundamentals of Wave Interaction
2.6 Interactions between Waves of the Same Family
2.7 Interactions between Waves of Different Families
2.8 Chromatographic Cycle for Two Solutes
2.9 Introduction to Displacement Development
2.10 Shock Layer Analysis
References
3. Hyperbolic Systems of First-Order Quasilinear Equations and Multicomponent Chromatography
3.1 Equations for the Equilibrium Chromatography of Many Solutes
3.2 Hyperbolic Systems of More than Two First-Order Equations
3.3 Generalized Riemann Invariants and Simple Waves
3.4 Riemann Problem and Fundamental Differential Equations
3.5 Langmuir Isotherm for Multicomponent Adsorption
3.6 Riemann Invariants for Multicomponent Chromatography with the Langmuir Isotherm
3.7 Characteristic Parameters and the space OMEGA(m)
3.8 Characteristic and Simple Waves
3.9 Discontinuities: Shocks
3.10 Entropy Change across a Shock
3.11 Solution of the Riemann Problem
3.12 Illustrations
References
4. Wave Interactions in Multicomponent Chromatography
4.1 Piecewise Constant Data and Patterns of Interaction
4.2 Interactions between Waves of the Same Family
4.3 Interactions between Waves of Different Families
4.4 Chromatographic Cycle for m Solutes
4.5 Multicomponent Separation by Displacement Development
4.6 An Example: Three Solute Separation by Displacement Development
References
5. Multicomponent Adsorption in Continuous Countercurrent Moving-Bed Adsorber
5.1 Basic Formulation
5.2 Theoretical Development for the Langmuir Isotherm
5.3 Analysis of Semi-Infinite Columns
5.4 Analysis of a Finite Column
5.5 Analysis of Wave Interactions
5.6 Illustrations
References
6. More on Hyperbolic Systems of Quasilinear Equations and Analysis of Adiabatic Adsorption Column
6.1 Equations for the Adiabatic Adsorption Column
6.2 Formulation for the Riemann Problem
6.3 Construction of a Continuous Solution
6.4 Discontinuities, Weak Solutions, and the Entropy Condition
6.5 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions
6.6 Solution Scheme for a Moving-Bed Problem
6.7 Adiabatic Adsorption of Single Solute
6.8 Adiabatic Adsorption of Two Solutes
6.9 Adiabatic Adsorption with Adsorptivity Reversal
6.10 Shock Layer Analysis of Adiabatic Adsorption References
7. Chemical Reaction in a countercurrent Reactor
7.1 General Formulation
7.2 Case of Two Reactants
7.3 Characteristics and Discontinuities for the Case of Two Reactants with Adsorption Equilibrium
7.4 The Steady State
7.5 General Procedure for Mapping Out the Steady-State Solution
7.6 Further Developments
References
Author Index; Subject Index