I have flipped through the first few pages of Evan's PDE book lately, and I am considering taking a graduate PDE course in the fall. However I don't really understand the purpose of PDE research. Not that I really understand the purpose of ODE research or even analysis research for that matter. Is analysis research basically the same thing as PDE research? What is the purpose/goal of studying PDE's? Why are they interested in existence/uniqueness? What else are the objectives, and why? What do they hope to obtain from doing PDE research? Do you study one particular PDE and find classes of solutions to it? Or do you study general PDE theory, and what do you hope to find?