Search

Showing total 2 results
2 results

1. A Free Boundary Problem for a Predator-Prey Model with Nonlinear Prey-Taxis.

Author

Yousefnezhad, Mohsen, Mohammadi, Seyyed Abbas, and Bozorgnia, Farid

Subjects
*REACTION-diffusion equations, *BOUNDARY value problems, *CLASSICAL solutions (Mathematics), *COMPUTER simulation, *NONLINEAR systems
Abstract

This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary and the stability of the solutions. [ABSTRACT FROM AUTHOR]

Published
2018
Full Text
View/download PDF

2. Mathematical Analysis and Pattern Formation for a Partial Immune System Modeling the Spread of an Epidemic Disease.

Author

Bendahmane, Mostafa and Saad, Mazen

Subjects
*PATTERN formation (Biology), *NUMERICAL analysis, *IMMUNE system, *EPIDEMICS, *MATHEMATICAL models, *PATHOGENIC microorganisms, *COMPUTER simulation, *BOUNDARY value problems
Abstract

Our motivation is a mathematical model describing the spatial propagation of an epidemic disease through a population. In this model, the pathogen diversity is structured into two clusters and then the population is divided into eight classes which permits to distinguish between the infected/uninfected population with respect to clusters. In this paper, we prove the weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary. Next, mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems. [ABSTRACT FROM AUTHOR]

Published
2011
Full Text
View/download PDF