An optimization problem and its application in population dynamics

DOI10.1090/proc/12873zbMath1381.35185OpenAlexW2215310269MaRDI QIDQ2790930

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Publication date: 8 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/12873

zbMATH Keywords

optimizationspatial heterogeneitytotal population

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Semilinear parabolic equations (35K58) Positive solutions to PDEs (35B09)

Related Items (20)

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology ⋮ 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 ⋮ Total biomass of a single population in two-patch environments ⋮ 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 ⋮ A single consumer model with Neumann boundary condition ⋮ Maximizing Metapopulation Growth Rate and Biomass in Stream Networks ⋮ On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition ⋮ Maximizing the total population with logistic growth in a patchy environment ⋮ 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 ⋮ Local dynamics of a diffusive predator-prey model in spatially heterogeneous environment ⋮ The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration ⋮ On the unboundedness of the ratio of species and resources for the diffusive logistic equation ⋮ Optimal location of resources maximizing the total population size in logistic models ⋮ Some Novel Results in Two Species Competition ⋮ Maximal total population of species in a diffusive logistic model ⋮ Spatial ecology, optimal control and game theoretical fishing problems

Cites Work

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• 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
• On the effects of migration and inter-specific competitions in steady state of some Lotka-Volterra model
• The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system I: Heterogeneity vs. homogeneity
• The evolution of slow dispersal rates: a reaction diffusion model
• Spatial heterogeneity of resources versus Lotka-Volterra dynamics
• On the effects of migration and spatial heterogeneity on single and multiple species
• Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I
• Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems

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