Titlebook: Introduction to Reaction-Diffusion Equations; Theory and Applicati King-Yeung Lam,Yuan Lou Textbook 2022 The Editor(s) (if applicable) and

木质

2193-4789 ematical biology.Based on a mini-course given at Institut He.This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts..The first part is an introduction to the maximum principle, the

巡回

Filibuster

The Principal Floquet Bundle for Parabolic Equationso proofs of the exponential separation property. One is based on the Harnack principle, and the other one relies on the generalized relative entropy. Finally,we introduce the notion of the normalized principal Floquet bundle, and derive the smooth dependence of the bundle on the coefficients in appropriate settings.

防锈

abysmal

Elements of Adaptive Dynamicsble strategy (ESS), continuously stable strategy, neighborhood invader strategy, dimorphism (coexistence of strategies) and evolutionary branching point, in concrete terms for a reaction-diffusion-advection model, supplemented by analytical results and examples.

现代

Selection-Mutation Modelsere the population is structured by trait and time only. In Section 10.2, we consider the problem of evolution of dispersal rate by incorporating the spatial variable in the model, and discuss a result of Perthame and Souganidis related to the evolution of slow dispersal in spatially heterogeneous and temporally constant environments.

有帮助

The Maximum Principle and the Principal Eigenvalues for Single Equations subsolutions in a generalized sense which enables the gluing of families super- or subsolutions. Next, we derive the existence of principal eigenvalue by applying the Krein–Rutman theorem. We will also determine the limit of principal eigenvalue as the diffusion rate tends to zero or infinity. Fina

一加就喷出

保守

The Maximum Principle and the Principal Eigenvalue for Systemsenvalue for cooperative elliptic/parabolic systems is considered, and the asymptotic behavior of the principal eigenvalues for small diffusion rates is determined. As an application, we apply the theory to a two-species competition system.

Polydipsia

The Principal Floquet Bundle for Parabolic Equationss a natural generalization of the principal eigenvalue when the coefficients for the equations are time-independent or time-periodic. Next, we give two proofs of the exponential separation property. One is based on the Harnack principle, and the other one relies on the generalized relative entropy.