Following [2], a model aiming at the description of two competing populations is introduced. In particular, it is considered a nonlinear system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for prey. The drift term in the equation for predators is in general a nonlocal and nonlinear function of the prey density: the movement of predators can hence be directed towards regions where the concentration of prey is higher. Lotka-Volterra type right hand sides describe the feeding. In [2] the resulting Cauchy problemis proved to be well posed in any space dimension with respect to the L1 topology, and estimates on the growth of the solution in L1 and L∞norm and on the time dependence are provided. Numerical integrations show a few qualitative features of the solutions. This is a joint work with RinaldoM. Colombo.
A mixed hyperbolic-parabolic system to describe predator-prey dynamics / Rossi, Elena. - In: BULLETIN BRAZILIAN MATHEMATICAL SOCIETY. - ISSN 1678-7544. - 47:2(2016), pp. 701-714. (Intervento presentato al convegno International Conference on Hyperbolic Problems IMPA : Theory, Numerics and Applications 28 july - 1 august tenutosi a Rio de Janeiro, Brasil nel 2014) [10.1007/s00574-016-0179-1].
A mixed hyperbolic-parabolic system to describe predator-prey dynamics
ROSSI, ELENA
2016
Abstract
Following [2], a model aiming at the description of two competing populations is introduced. In particular, it is considered a nonlinear system consisting of a nonlocal conservation law for predators coupled with a parabolic equation for prey. The drift term in the equation for predators is in general a nonlocal and nonlinear function of the prey density: the movement of predators can hence be directed towards regions where the concentration of prey is higher. Lotka-Volterra type right hand sides describe the feeding. In [2] the resulting Cauchy problemis proved to be well posed in any space dimension with respect to the L1 topology, and estimates on the growth of the solution in L1 and L∞norm and on the time dependence are provided. Numerical integrations show a few qualitative features of the solutions. This is a joint work with RinaldoM. Colombo.
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris
