| Description |
1 online resource (544) |
| Contents |
Cover13; -- 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 |
| Summary |
The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W 2p theory. Introductory explanations are included in the appendices for non-expert readers. The first chapter covers a wide range of steady-state and stability results involving pre |
| Subject |
Differential equations, Partial.
|
|
Differential equations, Nonlinear.
|
|
MATHEMATICS -- Differential Equations -- General.
|
|
Differential equations, Nonlinear
|
|
Differential equations, Partial
|
|
Nichtlineare partielle Differentialgleichung
|
| Form |
Electronic book
|
| ISBN |
1282758357 |
|
9781282758353 |
|
9789814277709 |
|
9814277703 |
|
