What are references for a second course in PDEs?

Question

I am interested in a slightly more advanced text in PDEs. I studied PDEs using Strauss' "Partial Differential Equations: An Introduction" and Farlow's "Partial Differential Equations for Scientists and Engineers". I have heard of Evans' book by I think it might be too advanced for my at this stage as my background is in engineering and not in mathematics. I am interested in something that helps me build my theoretical understanding,

Answer 1

In fact, due to its content (which includes introduction to Sobolev spaces, Galerkin method and semigroups), Part II of Evans (Chapters 5, 6 and 7) is a excellent source for a second course. In a sense, the approach is really introductory because it is done without the notion of distribution. However, I agree that it can be a hard reading (which doesn't mean you shouldn't try).

As an alternative with similar content (including introduction to distributions, Sobolev spaces, Galerkin method and semigroups), my suggestion is An Introduction to Partial Differential Equations by Renardy and Rogers. Maybe, you should start from Chapter 5. Note that chapters 6 and 8 are, basically, review of functional analysis (of course, focused on what will be needed) and thus the reading can become easier (in Evans book, the results and concepts from functional analysis are in the appendices without proofs or exercises).