Transport equation - one equation, plenty of methods

Opowiem o tylko z pozoru prostym równaniu transportu. Z jednej strony jest ono badane w kontekście istnienia i własności rozwiązań, a z drugiej strony jest częścią wielu modeli matematycznych opisujących procesy fizyczne i biologiczne.

 

I will discuss a transport equation, which is just seemingly simple. On one hand it is studied in the context of existence and properties of solutions. On the other hand it is a part of many mathematical models arisings from physics and biology. I will present an example of tissue growth model, where the problem of existence of solutions opens up a wide range of analytical methods. Among others, I will discuss the methods developed by Alessio Figalli - awarded this year the Fields medal.