Global solution for a general cross-diffusion two-competitive-predator and one-prey system with predator-taxis

DOI10.1016/j.cnsns.2020.105336zbMath1450.35139OpenAlexW3024782501WikidataQ115578233 ScholiaQ115578233MaRDI QIDQ2208133

Feng Dai, Bin Liu

Publication date: 23 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2020.105336

zbMATH Keywords

contraction mapping principle\(L^p\)-estimatesSchauder estimatesglobal existence and uniqueness

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for second-order parabolic systems (35K51) Classical solutions to PDEs (35A09)

Related Items (7)

Stationary and oscillatory patterns of a food chain model with diffusion and predator‐taxis ⋮ Hopf bifurcation of a delayed predator–prey model with Allee effect and anti-predator behavior ⋮ Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis ⋮ Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion ⋮ Global generalized solutions to a three species predator-prey model with prey-taxis ⋮ Steady state bifurcation of a population model with chemotaxis ⋮ Global solution and spatial patterns for a ratio-dependent predator-prey model with predator-taxis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis
• Avoidance behavior in intraguild predation communities: a cross-diffusion model
• Stationary and time-periodic patterns of two-predator and one-prey systems with prey-taxis
• Global existence of classical solutions to the cross-diffusion three-species model with prey-taxis
• Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
• Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis
• Global stability of prey-taxis systems
• Global solutions for a general strongly coupled prey-predator model
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• A diffusive predator-prey model with a protection zone
• Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems
• Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
• A reaction-diffusion system modeling predator-prey with prey-taxis
• Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
• Diffusion and ecological problems: Modern perspectives.
• Mathematical biology. Vol. 1: An introduction.
• Global dynamics for a diffusive predator-prey model with prey-taxis and classical Lotka-Volterra kinetics
• Pattern formation of a predator-prey model with the cost of anti-predator behaviors
• Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example
• Strong Allee effect in a diffusive predator-prey system with a protection zone
• Boundedness vs. blow-up in a chemotaxis system
• Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
• Global solution for a chemotactic–haptotactic model of cancer invasion
• L^PBounds of solutions of reaction-diffusion equations
• Spatial Ecology via Reaction‐Diffusion Equations
• A critical exponent in a degenerate parabolic equation
• Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis
• ANALYSIS OF A MATHEMATICAL MODEL OF TUMOR LYMPHANGIOGENESIS

This page was built for publication: Global solution for a general cross-diffusion two-competitive-predator and one-prey system with predator-taxis