Abstract: Front propagation in reaction-diffusion equations

Abstract: Front propagation in reaction-diffusion equations

In many real-world systems, the dominant behavior is determined by a mixture of spread ('diffusion') and growth ('reaction').  Two typical examples of this are population dynamics -- individuals naturally explore their environment and also produce offspring -- and chemical reactions -- heat diffuses and the reaction creates more heat.  The can be modelled mathematically using a class of partial differential equations called reaction-diffusion equations.  I will give an overview of various examples from this class, as well as the typical mathematical tools used to analyze them.