Finite time and global existence for solutions to some singular reaction-diffusion systems
LANGLAIS, Michel
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
LANGLAIS, Michel
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Discrete and Continuous Dynamical Systems - Series B. 2007, vol. 8, p. 61-72
American Institute of Mathematical Sciences
English Abstract
This note is dedicated to the question of global existence for so- lutions to a two component singular system of reaction–diffusion equations modeling predator–prey interactions in insular environments. Depending on a 2D ...Read more >
This note is dedicated to the question of global existence for so- lutions to a two component singular system of reaction–diffusion equations modeling predator–prey interactions in insular environments. Depending on a 2D parameter space, positive orbits of the underlying ODE system undergo interesting dynamics, e.g., finite time existence and global existence may co- exist. These results are partially extended to the reaction–diffusion system in the case of identical diffusivities. Our analysis relies on an auxiliary non singular reaction–diffusion system whose solutions may or may not blow up in finite time. Numerical simulations illustrate our analysis, including a numerical evidence of spatio–temporal oscillations.Read less <
English Keywords
global existence
blow–up time
oscillations
singular reaction–diffusion systems
predator–prey model in insular environment
invasion and persistence.
invasion and persistence
Origin
Hal imported