On one-dimensional chafee-infante equation

In this Master's thesis, we conduct a study of the one-dimensional Chafee-Infante partial differential equation on the interval [0, π]. This well-studied equation has applications in various physical processes, such as mass transport and particle diffusion. Our work consists of four parts. After introducing essential mathematical concepts, investigation begins with a deep dive into Sobolev spaces, focusing particularly on the one-dimensional case, to establish the necessary mathematical foundation. This is followed by a detailed examination of the one-dimensional heat equation. Building upon these sections, we discuss the properties of the Chafee-Infante equation from the viewpoint of the theory of partial differential equations.