On the unboundedness of the ratio of species and resources for the diffusive logistic equation

DOI10.3934/dcdsb.2020186zbMath1471.35276arXiv2001.06308OpenAlexW3034310827MaRDI QIDQ2033577

Jumpei Inoue, Kousuke Kuto

Publication date: 17 June 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06308

zbMATH Keywords

radial solutionselliptic equationsdiffusive logistic equationmathematical ecologysub-super solution method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Ecology (92D40) Positive solutions to PDEs (35B09)

Related Items (13)

ON THE RATIO OF BIOMASS TO TOTAL CARRYING CAPACITY IN HIGH DIMENSIONS ⋮ Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate ⋮ Impact of resource distributions on the competition of species in stream environment ⋮ Optimization of total population in logistic model with nonlocal dispersals and heterogeneous environments ⋮ Optimising the carrying capacity in logistic diffusive models: some qualitative results ⋮ Maximizing Metapopulation Growth Rate and Biomass in Stream Networks ⋮ The bang-bang property in some parabolic bilinear optimal control problems \textit{via} two-scale asymptotic expansions ⋮ On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition ⋮ A Fragmentation Phenomenon for a Nonenergetic Optimal Control Problem: Optimization of the Total Population Size in Logistic Diffusive Models ⋮ Limiting profile for stationary solutions maximizing the total population of a diffusive logistic equation ⋮ On the fragmentation phenomenon in the population optimization problem ⋮ Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: two-scale expansions and symmetrisations ⋮ Spatial ecology, optimal control and game theoretical fishing problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. II
• The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system. II: The general case
• Local dynamics of a diffusive predator-prey model in spatially heterogeneous environment
• The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system I: Heterogeneity vs. homogeneity
• On the dependence of population size upon random dispersal rate
• The effects of spatial heterogeneity in population dynamics
• On the effects of spatial heterogeneity on the persistence of interacting species
• Logistic Dirichlet problems with discontinuous coefficients.
• Maximization of the total population in a reaction-diffusion model with logistic growth
• Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. III
• Dynamics of a consumer-resource reaction-diffusion model. Homogeneous versus heterogeneous environments
• Persistence, competition, and evolution
• Optimal location of resources maximizing the total population size in logistic models
• Some monotone properties for solutions to a reaction-diffusion model
• Trait selection and rare mutations: the case of large diffusivities
• On the effects of migration and spatial heterogeneity on single and multiple species
• An optimization problem and its application in population dynamics
• Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I
• Diffusive logistic equations with indefinite weights: population models in disrupted environments
• Spatial Ecology via Reaction‐Diffusion Equations
• Some reaction diffusion models in spatial ecology
• Should a Park Be an Island?
• Diffusive logistic equations in population dynamics.

This page was built for publication: On the unboundedness of the ratio of species and resources for the diffusive logistic equation