Global existence of classical solutions to a predator–prey model with nonlinear prey-taxis

By Youshan Tao. 2010

194 citations recorded by the source corpus.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b99f94f91df070b9924ba87ddc8ed588d9ba636e

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Citations in the corpus

Predator–prey model with diffusion and indirect prey-taxis (2016, background): “The mathematical model of predator–prey interaction with prey-taxis was proposed for the first time by Kareiva and Odell(19) and later extended by other authors.(12,4,28,1,21,34) Prey-taxis allows predators to search prey more actively and thus it is expected to eliminate more effectively local conc”
Global stability of prey-taxis systems (2017, unknown): “In the existing works as recalled above, either the technical truncation assumption (see [1, 12,34]) or smallness assumption (see [46]) was imposed for the prey-taxis coefficient to ensure the global boundedness of solutions.”
Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “1) was studied by [1] (see also [7] for multi-species case), and the global existence and uniqueness of classical solutions in a smooth bounded domain ⊂Rn (n = 1, 2, 3) were obtained in [42].”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “…in Theorem 16 we have where (𝑢 ⋆ , 𝑣 ⋆ ) ∈ (0, ∞) × (0, 𝑠 0 ) is the unique solution of the algebraic system Precedents and close relatives concerned with questions of global solvability, boundedness and spatially homogeneous asymptotics in (CC7), and neighboring systems can be found in Refs.”
Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion (2019, result): “[2, 6, 22, 23, 37, 46]), and in particular the global existence and stability of solutions have been established in a previous work by the authors in Ref.”
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction (2017, background): “also [28], [12], [8], [16], [19], [29] and [21] for some closely related variants).”
Global bifurcation of solutions for a predator–prey model with prey‐taxis (2015, methodology): “The global existence and uniqueness of classical solutions to this model are studied by the contraction mapping principle together with Lp estimates and Schauder estimates of parabolic equations [4].”