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Author Leung, Anthony W
Title Nonlinear Systems Of Partial Differential Equations : Applications to Life and Physical Sciences
Imprint Singapore : World Scientific Publishing Company, 2009
book jacket
Descript 1 online resource (545 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- Contents -- Preface -- 1 Positive Solutions for Systems of Two Equations -- 1.1 Introduction -- 1.2 Strictly Positive Coexistence for Diffusive Prey-Predator Systems -- 1.3 Strictly Positive Coexistence for Diffusive Competing Systems -- 1.4 Strictly Positive Coexistence for Diffusive Cooperating Systems -- 1.5 Stability of Steady-States as Time Changes -- Part A: Prey-Predator Case. -- Part B: Competing Species Case. -- 2 Positive Solutions for Large Systems of Equations -- 2.1 Introduction -- 2.2 Synthesizing Large (Biological) Diffusive Systems from Smaller Subsystems -- 2.3 Application to Epidemics of Many Interacting Infected Species -- 2.4 Conditions for Coexistence in Terms of Signs of Principal Eigenvalues of Related Single Equations, Mixed Boundary Data -- 2.5 Positive Steady-States for Large Systems by Index Method -- 2.6 Application to Reactor Dynamics with Temperature Feedback -- 3 Optimal Control for Nonlinear Systems of Partial Differential Equations -- 3.1 Introduction and Preliminary Results for Scalar Equations -- 3.2 Optimal Harvesting-Coefficient Control of Steady-State Prey- Predator Diffusive Volterra-Lotka Systems -- 3.3 Time-Periodic Optimal Control for Competing Parabolic Systems -- 3.4 Optimal Control of an Initial-Boundary Value Problem for Fission Reactor Systems -- 3.5 Optimal Boundary Control of a Parabolic Problem -- 4 Persistence, Upper and Lower Estimates, Blowup, Cross-Diffusion and Degeneracy -- 4.1 Persistence -- 4.2 Upper-Lower Estimates, Attractor Set, Blowup -- 4.3 Diffusion, Self and Cross-Diffusion with No-Flux Boundary Condition -- 4.4 Degenerate and Density-Dependent Diffusions, Non-Extinction in Highly Spatially Heterogenous Environments -- Part A: Weak Upper and Lower Solutions for Degenerate or Non- Degenerate Elliptic Systems
Part B: Lower Bounds for Density-Dependent Di.usive Systems with Regionally Large Growth Rates. -- 5 TravelingWaves, Systems ofWaves, Invariant Manifolds, Fluids and Plasma -- 5.1 Traveling Wave Solutions for Competitive and Monotone Systems -- Part A: Existence of TravelingWave Connecting a Semi-Trivial Steady- State to a Coexistence Steady-State. -- Part B: Iterative Method for obtaining Traveling Wave for General Monotone Systems. -- 5.2 Positive Solutions for Systems of Wave Equations and Their Stabilities -- 5.3 Invariant Manifolds for Coupled Navier-Stokes and Second Order Wave Equations -- Part A: Main Theorem for the Existence of Invariant Manifold. -- Part B: Dependence on Initial Conditions, Asymptotic Stability of the Manifold, and Applications. -- 5.4 Existence and Global Bounds for Fluid Equations of Plasma Display Technology -- 6 Appendices -- 6.1 Existence of Solution between Upper and Lower Solutions for Elliptic and Parabolic Systems, Bifurcation Theorems -- 6.2 The Fixed Point Index, Degree Theory and Spectral Radius of Positive Operators -- 6.3 Theorems Involving Maximum Principle, Comparison and Principal Eigenvalues for Positive Operators -- 6.4 Theorems Involving Derivative Maps, Semigroups and Stability -- 6.5 W2,1 p Estimates, Weak Solutions for Parabolic Equations with Mixed Boundary Data, Theorems Related to Optimal Control, Cross-Diffusion and TravelingWave -- Bibliography -- Index
Key Features:Provides comprehensive presentation of theories concerning diffusion-reaction systems of interacting populations and their optimal controlMany easy-to-understand diagrams describing the range of parameters to insure the coexistence of many interacting species for convenient applicationIntroduces the developments on the subject from the early eighties to very recent results, with a large bibliography of references, and a convenient source of information for many researchers whose work may utilize such resultsServes to encourage and enlighten young students to create a deeper understanding on partial differential equationsIllustrates skillful use of upper-lower solutions, bifurcation, degree theory, semigroup, stability theorems, W p2, 1 theory and optimal control methodsIncludes new results in traveling waves and coupled systems of waves with fluid equations, applicable to electromagnetic theory and plasma display technology
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Leung, Anthony W Nonlinear Systems Of Partial Differential Equations: Applications To Life And Physical Sciences Singapore : World Scientific Publishing Company,c2009 9789814277693
Subject Differential equations, Partial.;Differential equations, Nonlinear
Electronic books
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