Introduction to reaction-diffusion equations : theory and applications to spatial ecology and evolutionary biology / / King-Yeung Lam and Yuan Lou

• Autore: Lam King-Yeung
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (316 pages)
• Disciplina: 780
• Soggetto topico: Mathematics; Equacions de reacció-difusió
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): LouYuan
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- Part I Linear Theory -- Chapter 1 The Maximum Principle and the Principal Eigenvalues for Single Equations -- 1.1 The Maximum Principle for Single Parabolic Equations -- 1.2 The Comparison Principle for Semilinear Equations -- 1.3 The Principal Eigenvalue for Linear Elliptic Operators -- 1.4 Further Reading -- Problems -- References -- Chapter 2 The Principal Eigenvalue for Periodic-Parabolic Problems -- 2.1 Existence of the Principal Eigenvalue for Periodic-Parabolic Problems -- 2.2 Qualitative Properties of Periodic Principal Eigenvalues -- 2.2.1 The Hutson-Shen-Vickers Lemma -- 2.2.2 Small diffusion limit -- 2.2.3 Large diffusion limit -- 2.2.4 Monotonicity in frequency -- 2.3 Applications to Two-Species Competition Models in a Spatially and Temporally Varying Environment -- 2.4 Further Reading -- Problems -- References -- Chapter 3 The Maximum Principle and the Principal Eigenvalue for Systems -- 3.1 Comparison Principle of Cooperative Parabolic Systems -- 3.2 The Principal Eigenvalue of Cooperative Systems -- 3.2.1 Existence results -- 3.2.2 Asymptotic behavior of the principal eigenvalue -- 3.3 Comparison Principle and Principal Eigenvalue for Competitive Parabolic Systems -- 3.4 Further Reading -- Problems -- References -- Chapter 4 The Principal Floquet Bundle for Parabolic Equations -- 4.1 Existence Results for Non-Divergence Form Parabolic Equations -- 4.2 Existence Results for Divergence Form Parabolic Equations -- 4.3 The Generalized Relative Entropy -- 4.4 Further Reading -- Problems -- References -- Part II Ecological Dynamics -- Chapter 5 The Logistic EquationWith Diffusion -- 5.1 A Reaction-Diffusion Model for a Single Species -- 5.2 The Logistic Equation -- 5.3 Critical Domain Size -- 5.4 Further Reading -- Problems -- References -- Chapter 6 Spreading in Homogeneous and Shifting Environments. ; 6.1 The Fisher-KPP Equation and the Definition of Spreading Speed -- 6.2 A Maximum Principle for Unbounded Domains -- 6.3 Homogeneous Environments -- Traveling wave solutions -- Periodically Varying Environments -- 6.4 Shifting Environments -- Shifting environments with a moving source patch -- Shifting boundary connecting an unbounded sink and an unbounded source patch -- Shifting boundary connecting two unbounded source patches and nonlocally pulling -- 6.5 Further Reading -- Problems -- References -- Chapter 7 The Lotka-Volterra Competition-Diffusion Systems for Two Species -- 7.1 Elements from the Theory of Monotone Dynamical Systems -- 7.2 Lotka-Volterra Systems with Constant Coefficients -- 7.3 Lotka-Volterra Systems with Heterogeneous Coefficients -- 7.3.1 Slow vs fast diffusing populations -- 7.3.2 Weak competition in a heterogeneous environment -- 7.4 Competition in an Advective Environment -- 7.5 Further Reading -- Problems -- References -- Chapter 8 Dynamics of Phytoplankton Populations -- 8.1 Introduction -- 8.2 Single Species in a EutrophicWater Column -- 8.2.1 Monotonicity of the single species model -- 8.2.2 Long-time dynamics of the single species model -- 8.3 Dynamics for Two Competing Phytoplankton Species -- Selection for more buoyant phytoplankton species -- 8.4 The N--Species Model - Application of the Principal Floquet Bundle -- 8.4.1 A priori estimates -- 8.4.2 A rough estimate -- 8.4.3 The normalized principal bundle -- 8.4.4 A general exclusion criterion -- 8.5 Further Reading -- Problems -- References -- Part III Evolutionary Dynamics -- Chapter 9 Elements of Adaptive Dynamics -- 9.1 Introduction -- 9.2 Evolution of Dispersal in Advective Environments -- The invasion exponent -- The selection gradient -- Singular strategy -- Convergence stable strategy -- Evolutionarily stable strategy -- Continuously stable strategy. ; Neighborhood invader strategy -- Dimorphism (coexistence of phenotypes) -- Evolutionary branching point -- 9.3 Further Reading -- Problems -- References -- Chapter 10 Selection-Mutation Models -- 10.1 Populations Structured by a Phenotypic Trait -- The Case Ω = RN -- 10.2 Populations Structured by Space and a Phenotypic Trait -- 10.3 Further Reading -- Problems -- References -- Appendices -- Appendix A The Fixed Point Index -- A.1 Properties of the Leray-Schauder Degree -- A.2 The Fixed Point Index -- References -- Appendix B The Krein-Rutman Theorem -- B.1 Introduction -- B.2 Cones and Orderings -- B.3 The Classical Krein-Rutman theorem -- B.4 The Generalized Krein-Rutman theorem for Homogeneous Maps -- B.5 Further Reading -- Problems -- References -- Appendix C Subhomogeneous Dynamics -- C.1 Subhomogeneous Maps -- C.2 Subhomogeneous Semiflows -- C.3 Further Reading -- Problems -- References -- Appendix D Existence of Connecting Orbits -- D.1 Discrete-Time Monotone Dynamical Systems -- D.2 Continuous-Time Monotone Dynamical Systems -- References -- Appendix E Abstract Competition Systems in Ordered Banach Spaces -- E.1 Discrete-Time Competition Systems -- E.2 Continuous-Time Competition Systems -- E.3 Further Reading -- Problems -- References -- Index.
• Titolo autorizzato: Introduction to Reaction-Diffusion Equations
• ISBN: 3-031-20422-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996503552803316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes on Mathematical Modelling in the Life Sciences