Existence and uniqueness of solutions of predator-prey type model with mixed boundary conditions

DOI10.1007/s10440-011-9630-xzbMath1233.35121OpenAlexW1999755596WikidataQ115605545 ScholiaQ115605545MaRDI QIDQ645009

L. Shangerganesh, Krishnan Balachandran

Publication date: 8 November 2011

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-011-9630-x

zbMATH Keywords

Schauder's fixed point theoremGronwall lemmapredator-prey spatially-structured modelreaction-diffusion-advection problems

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Weak solutions to PDEs (35D30) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis
• Existence and uniqueness results for a semilinear Black-Scholes type equation
• Weak and classical solutions to predator-prey system with cross-diffusion
• A reaction-diffusion system modeling predator-prey with prey-taxis
• Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source
• A free boundary problem modeling the cell cycle and cell movement in multicellular tumor spheroids
• Spatial segregation in competitive interaction-diffusion equations
• Local solutions to the Navier-Stokes equations with mixed boundary conditions
• On some anisotropic reaction-diffusion systems with \(L^{1}\)-data modeling the propagation of an epidemic disease
• Existence of solutions for reaction-diffusion systems with \(L^1\) data
• An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions.
• A mathematical analysis of a predator-prey system in a highly heterogeneous environment
• On the global existence of solutions to an aggregation model
• Prey-predator in patchy environment with cross diffusion
• Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions
• Boundedness vs. blow-up in a chemotaxis system
• Global solution for a chemotactic–haptotactic model of cancer invasion
• ANALYSIS OF A MATHEMATICAL MODEL OF TUMOR LYMPHANGIOGENESIS
• ON A TWO-SIDEDLY DEGENERATE CHEMOTAXIS MODEL WITH VOLUME-FILLING EFFECT
• On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowding
• Global existence for a parabolic chemotaxis model with prevention of overcrowding

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