Nonlinear systems of partial differential equations: applications to life and phyical sciences
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 532 S. graph. Darst. |
| ISBN: | 9789814277693 981427769X |
Internformat
MARC
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| 100 | 1 | |a Leung, Anthony W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear systems of partial differential equations |b applications to life and phyical sciences |c Anthony W. Leung |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XII, 532 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018613970 | ||
Datensatz im Suchindex
| _version_ | 1804140673937440768 |
|---|---|
| adam_text | Contents
Positive Solutions
for
Systems
of Two Equations
1
1.1
Introduction
.............................. 1
1.2
Strictly Positive Coexistence for Diffusive Prey-Predator Systems
4
1.3
Strictly Positive Coexistence for Diffusive Competing Systems
. . 26
1.4
Strictly Positive Coexistence for Diffusive Cooperating Systems
. 55
1.5
Stability of Steady-States as Time Changes
............ 74
Positive Solutions for Large Systems of Equations 111
2.1
Introduction
..............................
Ill
2.2
Synthesizing Large (Biological) Diffusive Systems from Smaller
Subsystems
.............................. 112
2.3
Application to Epidemics of Many Interacting Infected Species
. 124
2.4
Conditions for Coexistence in Terms of Signs of Principal Eigen¬
values of Related Single Equations, Mixed Boundary Data
.... 143
2.5
Positive Steady-States for Large Systems by Index Method
. . . 161
2.6
Application to Reactor Dynamics with Temperature Feedback
. . 178
Optimal Control for Nonlinear Systems of Partial Differential
Equations
197
3.1
Introduction and Preliminary Results for Scalar Equations
.... 197
3.2
Optimal Harvesting-Coefficient Control of Steady-State Prey-
Predator Diffusive Volterra-Lotka Systems
.............210
3.3
Time-Periodic Optimal Control for Competing Parabolic Systems
232
3.4
Optimal Control of an Initial-Boundary Value Problem for Fission
Reactor Systems
...........................258
3.5
Optimal Boundary Control of a Parabolic Problem
........269
Persistence, Upper and Lower Estimates, Blowup, Cross-Diffusion
and Degeneracy
289
4.1
Persistence
..............................289
4.2
Upper-Lower Estimates, Attractor Set, Blowup
..........309
xi
xii CONTENTS
4.3 Diffusion,
Self and Cross-Diffusion with No-Flux Boundary
Condition
...............................334
4.4
Degenerate and Density-Dependent Diffusions, Non-Extinction in
Highly Spatially Heterogenous Environments
...........362
5
Traveling Waves, Systems of Waves, Invariant Manifolds, Fluids
and Plasma
391
5.1
Traveling Wave Solutions for Competitive and Monotone Systems
391
5.2
Positive Solutions for Systems of Wave Equations and Their
Stabilities
...............................415
5.3
Invariant Manifolds for Coupled
Navier-
Stokes and Second Order
Wave Equations
............................434
5.4
Existence and Global Bounds for Fluid Equations of Plasma
Display Technology
..........................456
6
Appendices
481
6.1
Existence of Solution between Upper and Lower Solutions for
Elliptic and Parabolic Systems, Bifurcation Theorems
......481
6.2
The Fixed Point Index, Degree Theory and Spectral Radius of
Positive Operators
..........................485
6.3
Theorems Involving Maximum Principle, Comparison and Prin¬
cipal Eigenvalues for Positive Operators
..............489
6.4
Theorems Involving Derivative Maps, Semigroups and Stability
. 494
6.5
Wp Estimates, Weak Solutions for Parabolic Equations with
Mixed Boundary Data, Theorems Related to Optimal Control,
Cross-Diffusion and Traveling Wave
................502
Bibliography
507
Index
525
|
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| id | DE-604.BV035753969 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:43Z |
| institution | BVB |
| isbn | 9789814277693 981427769X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018613970 |
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| physical | XII, 532 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Leung, Anthony W. Verfasser aut Nonlinear systems of partial differential equations applications to life and phyical sciences Anthony W. Leung Singapore [u.a.] World Scientific 2009 XII, 532 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018613970&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leung, Anthony W. Nonlinear systems of partial differential equations applications to life and phyical sciences Differential equations, Nonlinear Differential equations, Partial Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4128900-6 |
| title | Nonlinear systems of partial differential equations applications to life and phyical sciences |
| title_auth | Nonlinear systems of partial differential equations applications to life and phyical sciences |
| title_exact_search | Nonlinear systems of partial differential equations applications to life and phyical sciences |
| title_full | Nonlinear systems of partial differential equations applications to life and phyical sciences Anthony W. Leung |
| title_fullStr | Nonlinear systems of partial differential equations applications to life and phyical sciences Anthony W. Leung |
| title_full_unstemmed | Nonlinear systems of partial differential equations applications to life and phyical sciences Anthony W. Leung |
| title_short | Nonlinear systems of partial differential equations |
| title_sort | nonlinear systems of partial differential equations applications to life and phyical sciences |
| title_sub | applications to life and phyical sciences |
| 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=018613970&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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