Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications

DOI10.1007/s00526-015-0838-xzbMath1331.35251OpenAlexW2024557649MaRDI QIDQ745562

Rui Peng, Xiao-Qiang Zhao

Publication date: 14 October 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-015-0838-x

zbMATH Keywords

diffusionadvectionprincipal eigenvaluephytoplanktonperiodic-parabolic eigenvalue problemnonlocal reaction-diffusion-advection equation

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with biology, chemistry and other natural sciences (35Q92)

Related Items (32)

The diffusive logistic model with a free boundary in a heterogeneous time-periodic environment ⋮ Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology ⋮ Principal eigenvalue and maximum principle for cooperative periodic-parabolic systems ⋮ Positive steady states of reaction-diffusion-advection competition models in periodic environment ⋮ Nonlocal dispersal equations in time-periodic media: principal spectral theory, limiting properties and long-time dynamics ⋮ A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species ⋮ Asymptotic behavior of the principal eigenvalue and the basic reproduction ratio for periodic patch models ⋮ A New Monotonicity for Principal Eigenvalues with Applications to Time-Periodic Patch Models ⋮ The diffusive logistic equation on periodically evolving domains ⋮ The generalised principal eigenvalue of time-periodic nonlocal dispersal operators and applications ⋮ Dynamics of a periodic-parabolic Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮ Novel spatial profiles of some diffusive SIS epidemic models ⋮ Coexistence and competitive exclusion in a time-periodic Lotka-Volterra competition-diffusion system ⋮ Concentration phenomenon of single phytoplankton species with changing-sign advection term ⋮ Spontaneous infection and periodic evolving of domain in a diffusive SIS epidemic model ⋮ Effects of depth and evolving rate on phytoplankton growth in a periodically evolving environment ⋮ Monotonicity and Global Dynamics of a Nonlocal Two-Species Phytoplankton Model ⋮ A reaction-diffusion-advection SIS epidemic model in a spatially-temporally heterogeneous environment ⋮ Existence, uniqueness, stability and bifurcation of periodic patterns for a seasonal single phytoplankton model with self-shading effect ⋮ Concentration behavior of endemic equilibrium for a reaction-diffusion-advection SIS epidemic model with mass action infection mechanism ⋮ Asymptotics of the Principal Eigenvalue for a Linear Time-Periodic Parabolic Operator I: Large Advection ⋮ Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Small/Large Diffusion Coefficient ⋮ Global structure of the periodic positive solutions for a general class of periodic-parabolic logistic equations with indefinite weights ⋮ Classifying the level set of principal eigenvalue for time-periodic parabolic operators and applications ⋮ Spatial diffusion and periodic evolving of domain in an SIS epidemic model ⋮ Competitive exclusion in a nonlocal reaction-diffusion-advection model of phytoplankton populations ⋮ Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator ⋮ Asymptotics of the principal eigenvalue for a linear time-periodic parabolic operator II: Small diffusion ⋮ Influence of mutations in phenotypically-structured populations in time periodic environment ⋮ Characterizing the existence of positive periodic solutions in the weighted periodic-parabolic degenerate logistic equation ⋮ The effects of diffusion on the principal eigenvalue for age-structured models with random diffusion ⋮ Asymptotic Behavior of the Basic Reproduction Ratio for Periodic Reaction-Diffusion Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the principal eigenvalue of linear cooperating elliptic systems with small diffusion
• Some paradoxical effects of the advection on a class of diffusive equations in ecology
• On the least point of the spectrum of certain cooperative linear systems with a large parameter
• The principal eigenvalue of a space-time periodic parabolic operator
• Phytoplankton depth profiles and their transitions near the critical sinking velocity
• An alternative approach to the Faber-Krahn inequality for Robin problems
• Critical conditions for phytoplankton blooms
• A theorem on elliptic differential inequalities with an application to gradient bounds
• Analysis of the self-shading effect on algal vertical distribution in natural waters
• Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics
• A priori bounds and multiple solutions for superlinear indefinite elliptic problems
• The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions
• Classifying smooth supersolutions for a general class of elliptic boundary value problems.
• The evolution of dispersal rates in a heterogeneous time-periodic environment
• Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer
• Sharp spatiotemporal patterns in the diffusive time-periodic logistic equation
• Long-time behavior of a cooperative periodic-parabolic system: temporal degeneracy versus spatial degeneracy
• Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena
• The effects of transport on the maximum principle
• A Faber-Krahn inequality for Robin problems in any space dimension
• On the principal eigenvalue of elliptic operators in \(\mathbb R^N\) and applications
• Estimates for the principal spectrum point for certain time-dependent parabolic operators
• The periodic logistic equation with spatial and temporal degeneracies
• Geometrical Structure of Laplacian Eigenfunctions
• A reaction–diffusion SIS epidemic model in a time-periodic environment
• On a nonlocal reaction–diffusion–advection equation modelling phytoplankton dynamics
• Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model
• Uniqueness in the Faber–Krahn Inequality for Robin Problems
• Exponential separation and principal Floquet bundles for linear parabolic equations on general bounded domains: Nondivergence case
• On the Asymptotic Behavior of the First Eigenvalue of a Second-Order Differential Operator with Small Parameter in Higher Derivatives
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Spatial Ecology via Reaction‐Diffusion Equations
• Effects of diffusion and advection on the smallest eigenvalue of an elliptic operator and their applications
• Eigenvalue Problems for a Cooperative System with a Large Parameter
• Linear Second Order Elliptic Operators
• Concentration Phenomena in a Nonlocal Quasi-linear Problem Modelling Phytoplankton I: Existence
• Concentration Phenomena in a Nonlocal Quasi-linear Problem Modelling Phytoplankton II: Limiting Profile
• Single Phytoplankton Species Growth with Light and Advection in a Water Column
• On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth
• Qualitative Analysis of a Cooperative Reaction-Diffusion System in a Spatiotemporally Degenerate Environment
• Dynamical systems in population biology

This page was built for publication: Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications