Concavity Method: A concise survey

Abstract

This short review article discusses the concavity method, one of the most effective ways to deal with parabolic equations with unbounded solutions in finite time. If the solution ceases to exist for some time, we say it blows up. The solution or some of its derivatives become singular depending on the equation. We focus on situations where the solution becomes unbounded in finite time, and our objective is to review some of the key blowup theory papers utilising the concavity method.