AN INTRODUCTION TO THE CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS

Abstract

Partial di erential equations play an important role in various elds of science like math ematics, physics, chemistry, etc. They are used to represent a physical phenomenon math ematically such as the propagation of heat or sound, thermodynamics, etc. Our main aim is to consider the wave and heat equations and observe how we can act on the trajectory of the solution by applying an appropriate control on the subset of the domain. We shall see, how we can build di erent type of controls and will discuss various properties of the wave and heat equations that makes the di erence in the controllability of both systems.