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Several physical phenomena are governed by nonlinear partial differential equations. Contrary to ordinary differential equations, the problems of existence and regularity of the solutions cannot be done in a unified way and one has to study each particular example. In this course, we want to focus on partial differential equations arising in many areas like combustion theory, population dynamics and biology. At the simplest level of modelization, these phenomena are described by reaction-diffusion equations.
The theory of this type of equation is far away from being fully understood but one can give however several results providing in some cases existence of solutions and their qualitative behaviour. An interesting property of these equations are that they carry a nice geometric insight.
If time permits, we might develop several topics related to research: homogenization, travelling waves in periodic media, integral diffusion, theory of free boundaries.
