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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 e cient 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-diffsion equations for RNA interactions. Journal of Mathematical Analysis and Applications, 425, 212-233, (2015). |
