A priori bounds and global existence of solutions of the steady-state Sel'kov model
By F. A. Davidson, Bryan P. Rynne. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
61 citations recorded by the source corpus.
Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/9d76cad7933516745eee9dc3abcebe713f004d18
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Citations in the corpus
- Non-constant positive steady states of the Sel'kov model ☆ (2003, methodology): “In the present paper, we consider p and l (or p and y) to be fixed, and y (or l )a s a bifurcation parameter, and give a different description from that of [ 7 ] for the existence of non-constant positive solutions to (1.2) under ‘‘weak’’ conditions (mi maybe multiple and some positive elements of f”
- Positive steady states of the Holling–Tanner prey–predator model with diffusion (2005, methodology): “These include the Gierer–Meinhardt model [11, 26], the Sel’kov model [ 5 , 25], the Brusselator model [2], the chemotactic diffusion model [24], the Lotka–Volterra competition model [14,15], the Lotka–Volterra predator–prey model [6,7,12,19,20], as well as models of semiconductors, plasmas, chemical”
- On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law (2008, unknown): “Recently, many works have been devoted to the mathematical analysis of this model; please refer to [5, 14, 20, 28] for the details of the discussion.”
- Strategy and stationary pattern in a three-species predator–prey model (2004, methodology): “These include the Gierer–Meinhardt model [14,18,39–41], the Sel’kov model [11,36], the Noyes–Field model for Belousov–Zhabotinskii reaction [31], the chemotactic diffusion model [21,38], the competition model [6,10,22–24], the predator–prey model [7,8,12,13,17,19,20,29,30,37], as well as models of s”
- Qualitative analysis of steady states to the Sel'kov model (2007, background): “Then, in [3], Davidson and Rynne obtained a priori upper bounds of positive classical solutions of (1.1) in the two cases where 0 p ∞ if n = 1 , 2, or 0 p 3 if n = 3.”
- Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion (2004, methodology): “These include the Gierer–Meinhardt model [11,18,38,41], the Sel’kov model [ 7 ,35], the Gray–Scott model [39], the Ginzburg–Landau equation [29], the Brusselator model [1], the Noyes–Field model for Belousov–Zhabotinskii reaction [32], the chemotactic diffusion model [22,37], the Lotka–Volterra comp”