Analysis Seminar - 16/12/2015

Wednesday, 16 December 2015, 2:00 p.m.

Lecturer: Farid Bozorgnia, CAMGSD-IST

Title: "Numerical investigation of spatially segregation models"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: In this talk, we consider different models of Reaction-Diffusion system which describe the interactions between biological components. These models are:

• Adjacent segregation: The adjacent segregation model has been studied extensively [2]. In this model particles annihilate on contact, and there is a common surface of separation.

• Segregation at distance: Recently in [1], the modeling of species that keep a positive distance is considered.

• Coupled Reaction-Diffusion Equations for RNA Interactions [3].

We review the known results and properties of these models. Then, we show existence and uniqueness of the solution for each model. Moreover, we use properties of limiting problem to construct efficient numerical simulations for elliptic and parabolic systems.

References

[1] L. Caffarelli, S. Patrizi and V. Quitalo, A nonlocal segregation model. Preprint.

[2] M. Conti, S. Terracini, and G. Verzini, Asymptotic estimate for spatial segregation of competitive systems. Advances in Mathematics. 195, 524-560,(2005).

[3] M. E. Hohn, B. Li, W. Yang, Analysis of coupled reaction-diffusion equations for RNA interactions. Journal of Mathematical Analysis and Applications, 425, 212-233, (2015).