An introduction to nonlinear partial differential equations:
While outstanding treatises on nonlinear partial differential equations do exist, beginning students seeking a fundamental understanding of their nature and application generally find these approaches to be too advanced
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY u.a.
Wiley
1994
|
| Series: | A Wiley interscience publication
Pure and applied mathematics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | While outstanding treatises on nonlinear partial differential equations do exist, beginning students seeking a fundamental understanding of their nature and application generally find these approaches to be too advanced David Logan's new text, the outgrowth of his many years as a professor at the University of Nebraska, resolves the dilemma by providing upper-level and graduate students in mathematics, engineering, and the physical sciences with a sensibly straightforward introduction to nonlinear PDEs, striking a balance between the mathematical and physical aspects of the subject An Introduction to Nonlinear Partial Differential Equations covers a wide range of applications, including biology, chemistry, porous media, combustion, detonation, traffic flow, water waves, plug flow reactors, and heat transfer, among other topics in applied mathematics |
| Physical Description: | XI, 400 S. graph. Darst. |
| ISBN: | 0471599166 |
Staff View
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| 520 | 3 | |a While outstanding treatises on nonlinear partial differential equations do exist, beginning students seeking a fundamental understanding of their nature and application generally find these approaches to be too advanced | |
| 520 | |a David Logan's new text, the outgrowth of his many years as a professor at the University of Nebraska, resolves the dilemma by providing upper-level and graduate students in mathematics, engineering, and the physical sciences with a sensibly straightforward introduction to nonlinear PDEs, striking a balance between the mathematical and physical aspects of the subject | ||
| 520 | |a An Introduction to Nonlinear Partial Differential Equations covers a wide range of applications, including biology, chemistry, porous media, combustion, detonation, traffic flow, water waves, plug flow reactors, and heat transfer, among other topics in applied mathematics | ||
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface ix
1. Partial Differential Equations 1
1.1. Partial Differential Equations, 2
1.2. Conservation Laws, 13
1.3. Constitutive Relations and Examples, 19
1.4. Initial and Boundary Value Problems, 26
1.5. Waves, 36
References, 48
2. First Order Equations and Characteristics 51
2.1. Linear First Order Equations, 51
2.2. Nonlinear Equations, 56
2.3. Quasilinear Equations, 60
2.4. Propagation of Singularities, 65
2.5. General First Order Equation, 71
2.6. Uniqueness Result, 77
References, 79
3. Weak Solutions to Hyperbolic Equations 80
3.1. Discontinuous Solutions, 81
3.2. Shock Formation, 92
3.3. Traffic Flow; Plug Flow Reactors, 99
3.4. Weak Solutions: A Formal Approach, 108
3.5. Asymptotic Behavior of Shocks, 116
References, 125
4. Diffusion Processes 126
4.1. Review of Basic Results, 127
4.2. Similarity Methods, 134
4.3. Nonlinear Diffusion Models, 141
vii
viii CONTENTS
4.4. Reaction Diffusion; Fisher s Equation, 151
4.5. Convection Diffusion; Burgers Equation, 161
4.6. Asymptotic Solutions to Burgers Equation, 166
Appendix: Phase Plane, 173
References, 182
5. Hyperbolic Systems 184
5.1. Waves in Shallow Water; Gas Dynamics, 184
5.2. Hyperbolic Systems and Characteristics, 194
5.3. Riemann s Method, 205
5.4. Hodographs; Wavefronts, 217
5.5. Weakly Nonlinear Approximations, 227
References, 233
6. Reaction Diffusion Equations 234
6.1. Reaction Diffusion Models, 235
6.2. Traveling Wave Solutions, 244
6.3. Existence of Solutions, 257
6.4. Maximum Principles and Comparison Theorems, 274
6.5. Energy Estimates and Asymptotic Behavior, 282
References, 299
7. Models for Chemically Reacting Fluids 301
7.1. Equations of Reactive Flow, 302
7.2. Reactive Flow Models, 315
7.3. Detonation Waves, 326
7.4. Combustion, 344
References, 354
8. Elliptic Equations 356
8.1. Elliptic Equations and Models, 357
8.2. Basic Results for Elliptic Operators, 366
8.3. Eigenvalue Problems, 372
8.4. Stability and Bifurcation, 378
References, 394
Index 397
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:43:41Z |
| institution | BVB |
| isbn | 0471599166 |
| language | English |
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| physical | XI, 400 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Wiley |
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| series2 | A Wiley interscience publication Pure and applied mathematics |
| spelling | Logan, J. David 1944- Verfasser (DE-588)120361000 aut An introduction to nonlinear partial differential equations J. David Logan New York, NY u.a. Wiley 1994 XI, 400 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley interscience publication Pure and applied mathematics While outstanding treatises on nonlinear partial differential equations do exist, beginning students seeking a fundamental understanding of their nature and application generally find these approaches to be too advanced David Logan's new text, the outgrowth of his many years as a professor at the University of Nebraska, resolves the dilemma by providing upper-level and graduate students in mathematics, engineering, and the physical sciences with a sensibly straightforward introduction to nonlinear PDEs, striking a balance between the mathematical and physical aspects of the subject An Introduction to Nonlinear Partial Differential Equations covers a wide range of applications, including biology, chemistry, porous media, combustion, detonation, traffic flow, water waves, plug flow reactors, and heat transfer, among other topics in applied mathematics Differential equations, Nonlinear Differential equations, Partial Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006589170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Logan, J. David 1944- An introduction to nonlinear partial differential equations Differential equations, Nonlinear Differential equations, Partial Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4128900-6 |
| title | An introduction to nonlinear partial differential equations |
| title_auth | An introduction to nonlinear partial differential equations |
| title_exact_search | An introduction to nonlinear partial differential equations |
| title_full | An introduction to nonlinear partial differential equations J. David Logan |
| title_fullStr | An introduction to nonlinear partial differential equations J. David Logan |
| title_full_unstemmed | An introduction to nonlinear partial differential equations J. David Logan |
| title_short | An introduction to nonlinear partial differential equations |
| title_sort | an introduction to nonlinear partial differential equations |
| topic | Differential equations, Nonlinear Differential equations, Partial Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Differential equations, Nonlinear Differential equations, Partial Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006589170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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