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Mathematical Modeling in Biology

Since
several years, mathematical modelling of biological phenomena has become of a great interest. In particular, many phenomena are well described thanks to partial differential equations (PDE).
The aim of this course is to present to master’s student several PDE models that describe different biological phenomena and their analysis. It will be divided into several parts:

  1. Basic modelling in Biology. In this first part, we will introduce some simple examples of mathematical models in biology.
  2. Basic mathematical tools. In this second part, we will present usefull mathematical tools for the study of PDE models: parabolic equations, transport equations in biology.
  3. Mathematical analysis. Several aspects arising in PDE models will be studied: traveling waves for Fisher/KPP equation, Foker-Planck equation, blow-up phenomena, linear instability.

Referências:
BRÉZIS, H. – Analyse fonctionnelle, théorie et applications. Masson, 1983.
EVANS, L.C. – Partial Differential Equations, Graduate Studies in Mathematics, Vol 19, American Mathematical Society (1998).
MURRAY, J.D. – Mathematical biology, Vol 1 and 2, Second edition. Springer, 2002.
PERTHAME, B. -Transport equations arising in biology, L.N. Series ‘Frontiers in mathematics’, Birkhauser, 2007.
PERTHAME, B. – Growth, reaction, movement and diffusion from biology, M2 course, UPMC.

 

* Ementa básica. O professor tem autonomia para efetuar qualquer alteração.